Загрузка страницы
Все видеоНовые видеоПопулярные видеоКатегории видео

Ellipses - Example 1: Sketching 4x^2 + 9y^2 = 36

4x^2 + 9y^2 = 36 is the equation of an ellipse centred at the origin (0,0). Before we can sketch the ellipse, we need to find the vertices (i.e. the x and y intercepts) by transforming the equation to the standard form, which is:

x^2/a^2 + y^2/b^2

where...

a is the semi-major axis
b is the semi-minor axis

So, dividing the equation by 36, we get:

x^2/9 + y^2/4 = 1

Or...

x^2/3^2 + y/2^2 = 1

Thus a = 3 and b = 2, and hence the vertices are:

A = (3,0)
A' = (-3,0)
B = (0,2)
B' = (0,-2)

To fully define the ellipse, we should also find the focal points and the directrices. Thus we to find the eccentricity. We can do this through the relationship:

b^2 = a^2 - (ae)^2

The focal points (foci) are given by:

F = (ae,0)
F' = (-ae,0)

And the equations are of the directrices are:

x = a/e
x = -a/e

Suggested video:
- "Conic Sections: The Ellipse - Part 1" https://youtu.be/j3abHkwAFvY
Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.

Please ask me a maths question by commenting below and I will try to help you in future videos.

Follow me on Twitter! twitter.com/MasterWuMath

Видео Ellipses - Example 1: Sketching 4x^2 + 9y^2 = 36 канала MasterWuMathematics
Показать
Комментарии отсутствуют
Введите заголовок:

Введите адрес ссылки:

Введите адрес видео с YouTube:

Зарегистрируйтесь или войдите с
Информация о видео
14 декабря 2015 г. 16:38:09
00:08:31
MasterWuMathematics
Теги
Правообладателям
Жалоба
Комментарии
Другие видео канала
Derivative of cos^2(x) - d/dx [cos^2(x)] - Chain Rule and Half Angle FormulaDerivative of cos^2(x) - d/dx [cos^2(x)] - Chain Rule and Half Angle FormulaCompound Interest: How much can you earn in 3 years at 9 per cent?Compound Interest: How much can you earn in 3 years at 9 per cent?How to integrate ∫csc^3(x)dx - (Integration By Parts)How to integrate ∫csc^3(x)dx - (Integration By Parts)Limit of (2 + h)^3 - 8 / h as h approaches 0Limit of (2 + h)^3 - 8 / h as h approaches 0What is the derivative of tan^2(x)? - d/dx[tan^2(x)]What is the derivative of tan^2(x)? - d/dx[tan^2(x)]Trig and Complex Numbers - Power Reduction IdentitiesTrig and Complex Numbers - Power Reduction IdentitiesInverse hyperbolic cosine [cosh^-1(x)] as a logarithmInverse hyperbolic cosine [cosh^-1(x)] as a logarithmHow to evaluate the limit sqrt(1 + h) - 1 / h as x approaches 0How to evaluate the limit sqrt(1 + h) - 1 / h as x approaches 0Integral of ∫ sin(4x) / cos^4(x) dxIntegral of ∫ sin(4x) / cos^4(x) dxTrig and Complex Numbers - Multiple Angle IdentitiesTrig and Complex Numbers - Multiple Angle IdentitiesDerivative of csc(x) - Reciprocal RuleDerivative of csc(x) - Reciprocal RuleEvaluating the Integral ∫ sqrt(x) / x^2 + x dx on the interval [1/3, 3]Evaluating the Integral ∫ sqrt(x) / x^2 + x dx on the interval [1/3, 3]Proof: Reciprocal Rule of Differentiation by First PrinciplesProof: Reciprocal Rule of Differentiation by First PrinciplesLimit of (x^2 + x - 6) / (x - 2) as x approaches 2Limit of (x^2 + x - 6) / (x - 2) as x approaches 2How to Integrate ∫ log_a(x) dxHow to Integrate ∫ log_a(x) dxDerivative of arcsin(x) - d/dx [ sin^-1(x) ] - Inverse Sine functionDerivative of arcsin(x) - d/dx [ sin^-1(x) ] - Inverse Sine functionHow to Integrate ∫xsin^3(x)cos^4(x)dxHow to Integrate ∫xsin^3(x)cos^4(x)dxIntegral of ∫ acos(x) / b + acos(x) dx with t = tan(x/2)Integral of ∫ acos(x) / b + acos(x) dx with t = tan(x/2)How to integrate ∫ dx / (a^2 + b^2x^2)How to integrate ∫ dx / (a^2 + b^2x^2)How to Integrate ∫ a^x dxHow to Integrate ∫ a^x dxFind a and b for ax^3 - 8x^2 - 9x + b: Polynomial Remainder TheoremFind a and b for ax^3 - 8x^2 - 9x + b: Polynomial Remainder Theorem
Статистика портала
Яндекс.Метрика
© 2008-2024 «Информационно-развлекательный портал города Верхняя Салда»
| Карта портала | Реклама | Контакты | Сообщить об ошибке | Соглашения
salda.ws salda.ws@mail.ru
Сейчас на сайте: 512 Статистика портала