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উদ্দীপকের আলোকে নিচের দুইটি প্রশ্নের উত্তর দাও

4y² - 5x² = 20 একটি অধিবৃত্তের সমীকরণ।

অধিবৃত্তটির অসীমতট রেখার সমীকরণ কোনটি?

Created: 1 year ago | Updated: 3 months ago

Updated: 3 months ago

$y = \pm \frac{\sqrt{5}}{2} x$

$y = \pm \frac{2}{\sqrt{5}} x$

$x = \pm \frac{\sqrt{5}}{2} y$

$x = \pm \frac{2}{\sqrt{5}} y$

একাদশ- দ্বাদশ শ্রেণি কুমিল্লা বোর্ড উচ্চতর গণিত

Description

523

অধিবৃত্তটির অসীমতট রেখার সমীকরণ কোনটি?

| এর সঠিক উত্তর $y = \pm \frac{\sqrt{5}}{2} x$

Earn by contributing to add descriptions.

উচ্চতর গণিত

Please, contribute to add content.

Messages Timeline Exceptions Views33 Route Queries29 Models28 Livewire0 Mails Gate Session Request

Request history8.2.27142ms35MBGET academy/single-question

Booting (83.38ms)time
Application (58.14ms)time
1 x Booting (58.92%)
83.38ms
1 x Application (41.08%)
58.14ms

33 templates were rendered

questions.mcq.single_questionsingle_question.blade.php#?blade
questions.include.show_timeshow_time.blade.php#?blade
questions.mode.readingreading.blade.php#?blade
questions.include.activity_layoutactivity_layout.blade.php#?blade
questions.mcq.sidebarsidebar.blade.php#?blade
common.modal.bookmark_modalbookmark_modal.blade.php#?blade
common.modal.tag_add_modaltag_add_modal.blade.php#?blade
common.modal.add_description_modaladd_description_modal.blade.php#?blade
common.modal.video_modalvideo_modal.blade.php#?blade
common.modal.edit_description_modaledit_description_modal.blade.php#?blade
common.modal.error_report_modalerror_report_modal.blade.php#?blade
job.job_include.job_scriptjob_script.blade.php#?blade
common.script.activity_scriptactivity_script.blade.php#?blade
common.script.navigator_sharenavigator_share.blade.php#?blade
common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
layouts.single-question-appsingle-question-app.blade.php#?blade
includes.single_header_linksingle_header_link.blade.php#?blade
common.login_modallogin_modal.blade.php#?blade
components.authentication-card-logoauthentication-card-logo.blade.php#?blade
layouts.headerheader.blade.php#?blade
layouts.toolbartoolbar.blade.php#?blade
layouts.footerfooter.blade.php#?blade
common.includes.promotion_modalpromotion_modal.blade.php#?blade
common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
includes.footer_link2footer_link2.blade.php#?blade
includes.restrictrestrict.blade.php#?blade
livewire-alert::components.scriptsscripts.blade.php#?blade
livewire-alert::components.flashflash.blade.php#?blade
admin.include.toastrtoastr.blade.php#?blade
common.search.search_scriptsearch_script.blade.php#?blade
common.script.promotion_scriptpromotion_script.blade.php#?blade
common.script.promotion_functionspromotion_functions.blade.php#?blade

uri: GET academy/single-question
middleware: web, throttle:global
controller: App\Http\Controllers\Academy\QuestionController@singleMcq
namespace
prefix
where
as: academy.single-question
file: app/Http/Controllers/Academy/QuestionController.php:62-98

29 statements were executed24.23ms

QuestionController.php#190debugerror_satt610μsupdate `questions` set `view_count` = `view_count` + 1 where `id` = 305261

Bindings	0: 305261
Backtrace	app/Http/Controllers/Academy/QuestionController.php:190 vendor/laravel/framework/src/Illuminate/Cache/Lock.php:95 app/Http/Controllers/Academy/QuestionController.php:187 app/Http/Controllers/Academy/QuestionController.php:79 vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54

QuestionController.php#256debugerror_satt330μs

select `id`, `view_count`, `vote`, `subject_id`, `category_id`, `sub_category_id`, `board_exam_id`, `passage_id`, `question_type`, `question`, `is_duplicate`, `status`, `image`, `meta_og_image`, `meta_og_title`, `meta_keyword`, `created_at`, `updated_at`, exists(select * from `review_contents` where `questions`.`id` = `review_contents`.`reviewable_id` and `review_contents`.`reviewable_type` = 'App\\Models\\Question') as `review_content_exists` from `questions` where `id` = '305261' and `questions`.`deleted_at` is null limit 1

Bindings	0: App\Models\Question 1: 305261
Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt160μs

select `id`, `question_id`, `option_1`, `option_2`, `option_3`, `option_4`, `option_5`, `image_option`, `image_question`, `answer` from `question_options` where `question_options`.`question_id` in (305261) and `question_options`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt230μsselect `id`, `title`, `passage` from `passages` where `passages`.`id` in (3926) and `passages`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt110μs

select `id`, `name`, `slug`, `meta_og_image` from `sub_categories` where `sub_categories`.`id` in (4878) and `sub_categories`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt120μs

select `id`, `name`, `des_updated_by`, `des_added_by`, `link_subject_id`, `slug` from `subjects` where `subjects`.`id` in (74) and `subjects`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt210μs

select `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (74) and `subject_descriptions`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt170μs

select `subjects`.`id`, `subjects`.`name`, `subjects`.`slug`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, `subjectables`.`created_user_id` as `pivot_created_user_id`, `subjectables`.`deleted_at` as `pivot_deleted_at`, `subjectables`.`status` as `pivot_status`, `subjectables`.`created_at` as `pivot_created_at`, `subjectables`.`updated_at` as `pivot_updated_at` from `subjects` inner join `subjectables` on `subjects`.`id` = `subjectables`.`subject_id` where `subjectables`.`subjectable_id` in (305261) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt110μsselect * from `vote_statistics` where `vote_statistics`.`question_id` in (305261)

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt240μs

select * from `descriptions` where `descriptions`.`descriptionable_id` in (305261) and `descriptions`.`descriptionable_type` = 'App\\Models\\Question' and `status` in ('approve', 'active') and `descriptions`.`deleted_at` is null order by `vote` desc

Bindings	0: App\Models\Question 1: approve 2: active
Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt110μsselect `id`, `board_id` from `board_exams` where `board_exams`.`id` in (1231) and `board_exams`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt100μsselect `id`, `name` from `boards` where `boards`.`id` in (6) and `boards`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt90μs

select `id`, `bookmarkable_id`, `bookmarkable_type`, `user_id` from `bookmarks` where `bookmarks`.`bookmarkable_id` in (305261) and `bookmarks`.`bookmarkable_type` = 'App\\Models\\Question' and `user_id` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt90μs

select `id`, `votable_id`, `votable_type`, `user_id` from `votes` where `votes`.`votable_id` in (305261) and `votes`.`votable_type` = 'App\\Models\\Question' and `user_id` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#256debugerror_satt80μs

select `id`, `question_id`, `user_id`, `choosen_option` from `vote_logs` where `vote_logs`.`question_id` in (305261) and `user_id` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:256 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:208 app/Http/Controllers/Academy/QuestionController.php:82

QuestionController.php#375debugerror_satt80μs

select `id`, `name`, `_lft`, `_rgt`, `parent_id`, `des_updated_by`, `des_added_by`, `slug`, `link_subject_id` from `subjects` where 0 = 1 and `subjects`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:375 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:345 app/Http/Controllers/Academy/QuestionController.php:85

QuestionController.php#451debugerror_satt110μs

select `id`, `view_count`, `vote`, `subject_id`, `category_id`, `sub_category_id`, `board_exam_id`, `passage_id`, `question_type`, `question`, `is_duplicate`, `status`, `image`, `created_at`, `updated_at` from `questions` where 0 = 1 and `id` != 305261 and `questions`.`deleted_at` is null order by `created_at` desc limit 6

Bindings	0: 305261
Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:411 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt19.83ms

select `id`, `view_count`, `vote`, `subject_id`, `category_id`, `sub_category_id`, `board_exam_id`, `passage_id`, `question_type`, `question`, `is_duplicate`, `status`, `image`, `created_at`, `updated_at` from `questions` where `subject_id` = 74 and `id` != 305261 and `questions`.`deleted_at` is null order by `created_at` desc limit 6

Bindings	0: 74 1: 305261
Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt230μs

select * from `question_options` where `question_options`.`question_id` in (448433, 448434, 448435, 448436, 448437, 448493) and `question_options`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt110μsselect `id`, `name`, `slug` from `subjects` where `subjects`.`id` in (74) and `subjects`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt100μs

select `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (6191) and `sub_categories`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt100μsselect `id`, `name` from `categories` where `categories`.`id` in (95) and `categories`.`deleted_at` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt200μs

select `subjects`.`id`, `subjects`.`name`, `subjects`.`slug`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, `subjectables`.`created_user_id` as `pivot_created_user_id`, `subjectables`.`deleted_at` as `pivot_deleted_at`, `subjectables`.`status` as `pivot_status`, `subjectables`.`created_at` as `pivot_created_at`, `subjectables`.`updated_at` as `pivot_updated_at` from `subjects` inner join `subjectables` on `subjects`.`id` = `subjectables`.`subject_id` where `subjectables`.`subjectable_id` in (448433, 448434, 448435, 448436, 448437, 448493) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt120μs

select * from `vote_statistics` where `vote_statistics`.`question_id` in (448433, 448434, 448435, 448436, 448437, 448493)

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt90μs

select `id`, `bookmarkable_id`, `bookmarkable_type`, `user_id` from `bookmarks` where `bookmarks`.`bookmarkable_id` in (448433, 448434, 448435, 448436, 448437, 448493) and `bookmarks`.`bookmarkable_type` = 'App\\Models\\Question' and `user_id` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt80μs

select `id`, `votable_id`, `votable_type`, `user_id` from `votes` where `votes`.`votable_id` in (448433, 448434, 448435, 448436, 448437, 448493) and `votes`.`votable_type` = 'App\\Models\\Question' and `user_id` is null

Bindings	0: App\Models\Question
Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

QuestionController.php#451debugerror_satt70μs

select `id`, `question_id`, `user_id`, `choosen_option` from `vote_logs` where `vote_logs`.`question_id` in (448433, 448434, 448435, 448436, 448437, 448493) and `user_id` is null

Backtrace	app/Http/Controllers/Academy/QuestionController.php:451 app/Http/Controllers/Academy/QuestionController.php:414 vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427 vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453 app/Http/Controllers/Academy/QuestionController.php:402

single_question.blade.php#85debugerror_satt180μsselect * from `categories` where `categories`.`id` = 130 and `categories`.`deleted_at` is null limit 1

Bindings	0: 130
Backtrace	view::questions.mcq.single_question:85 vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124 vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22 vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75

restrict.blade.php#30debugerror_satt170μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null

Bindings	0: active
Backtrace	view::includes.restrict:30 vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124 vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22 vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75

App\Models\Question: 7Question.php#?
App\Models\QuestionOption: 7QuestionOption.php#?
App\Models\PackagePlan: 4PackagePlan.php#?
App\Models\SubCategory: 2SubCategory.php#?
App\Models\Subject: 2Subject.php#?
App\Models\Category: 2Category.php#?
App\Models\Passage: 1Passage.php#?
App\Models\SubjectDescription: 1SubjectDescription.php#?
App\Models\BoardExam: 1BoardExam.php#?
App\Models\Board: 1Board.php#?

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_previous: array:1 [ "url" => "https://debugerror.xyz/academy/single-question?ques_id=305261" ]
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/academy/single-question

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OK

format

html

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text/html; charset=UTF-8

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[]

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	Date ↕	Method	URL	Data
#1	2025-03-13 21:46:37	GET	/academy/single-question?ques_id=305261	33 29 28