CONIQUE en coordonnées polaire

Mathématique - 6ème Construction

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CONIQUE en coordonnées polaire

Matériel didactique : craie de couleur

Objectif opérationnel : A la fin de leçon, l'élève sera capable de déterminer l'équation d'une conique en coordonnées polaires.

Rappel

Comment s'écirt l'équation d'une conique en coordonnées homogènes, cette équation s'écrit:

Rappel

L'équation homogène s'écrit: f(x,y,z)≡Ay²+2Bxy+Cx²+2Dyz+2Exz+Fz²=0.

Motivation

Déterminez la forme générale de l'équation générale d'une conique.

Motivation

La forme générale de l'équation générale d'une conique est: Ay²+2(Bx+D)y+Cx²+2Ex+F=0

Annonce du sujet

Qu'allons-nous étudier aujourd'hui ?

Annonce du sujet

Aujourd'hui, nous allons étudier la conique en coordonnées polaires.

Analyse

Qu'entendez-vous par conique en coordonnées polaires?

Analyse

Quelle est la formule de la conique en coordonnées polaires?

Après le développement, le triangle étant rectangle le formule est :

Messages Timeline Exceptions Views7 Route Queries36 Models48 Gate Session Request

8.1.28140ms6MBGET lessons/{id}/{slug}

Booting (36.09ms)
Application (104ms)
1 x Application (74.1%)
103.50ms
1 x Booting (25.84%)
36.09ms

7 templates were rendered

public.lessons.show (resources/views/public/lessons/show.blade.php)2bladefile
Params
0
lesson
1
lessons
components.banner-page (resources/views/components/banner-page.blade.php)7bladefile
Params
0
property
1
firstTitle
2
secondTitle
3
src
4
attributes
5
slot
6
__laravel_slots
components.ad-card-lesson-long (resources/views/components/ad-card-lesson-long.blade.php)7bladefile
Params
0
summary
1
title
2
actionLink
3
actionText
4
attributes
5
slot
6
__laravel_slots
components.button-link (resources/views/components/button-link.blade.php)6bladefile
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0
class
1
title
2
href
3
attributes
4
slot
5
__laravel_slots
layouts.public (resources/views/layouts/public.blade.php)10bladefile
Params
0
__env
1
app
2
errors
3
lesson
4
lessons
5
component
6
__currentLoopData
7
lesson_
8
loop
9
section
layouts.include.public.header (resources/views/layouts/include/public/header.blade.php)10bladefile
Params
0
__env
1
app
2
errors
3
lesson
4
lessons
5
component
6
__currentLoopData
7
lesson_
8
loop
9
section
layouts.include.public.footer (resources/views/layouts/include/public/footer.blade.php)10bladefile
Params
0
__env
1
app
2
errors
3
lesson
4
lessons
5
component
6
__currentLoopData
7
lesson_
8
loop
9
section

Params
0	`lesson`
1	`lessons`

Params
0	`property`
1	`firstTitle`
2	`secondTitle`
3	`src`
4	`attributes`
5	`slot`
6	`__laravel_slots`

Params
0	`summary`
1	`title`
2	`actionLink`
3	`actionText`
4	`attributes`
5	`slot`
6	`__laravel_slots`

Params
0	`class`
1	`title`
2	`href`
3	`attributes`
4	`slot`
5	`__laravel_slots`

Params
0	`__env`
1	`app`
2	`errors`
3	`lesson`
4	`lessons`
5	`component`
6	`__currentLoopData`
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8	`loop`
9	`section`

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3	`lesson`
4	`lessons`
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9	`section`

uri: GET lessons/{id}/{slug}
middleware: web
controller: App\Http\Controllers\Public\LessonController@show
as: public.lesson.show
namespace
prefix: /lessons
where
file: app/Http/Controllers/Public/LessonController.php:86-138

36 statements were executed55.56ms

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select * from `content_texts` where `content_texts`.`id` = 66169 and `content_texts`.`deleted_at` is null limit 1

280μsview::public.lessons.show:133schoolap

Metadata
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Backtrace	20. view::public.lessons.show:133 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195

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App\Models\Lesson\Lesson: 5

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