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Parametric equation of Ellipse - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Parametric equation of Ellipse is considered one the most difficult concept.

  • 48 Questions around this concept.

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QuestionEASY

Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis.  If its eccentricity is \small \frac{3}{5}  and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the end points of major and minor axes of ellipse, is

 

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The equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity \sqrt{\frac{2}{5}}   is

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The equation of the circle passing through the foci of the ellipse \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 , and having centre at

(0, 3) is :

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The foci of the ellipse \mathrm{25(x+1)^2+9(y+2)^2=225} are: 

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Concepts Covered - 1

Parametric equation of Ellipse

Parametric equation of Ellipse:

The equations x = a cosӨ, y = b sinӨ are called the parametric equation of the ellipse.

The circle described on the major axis as the diameter is called the auxiliary circle.

\\ {\text {Equation of Ellipse is } \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1} \\ {\text { Then, equation of auxiliary circle is } x^{2}+y^{2}=a^{2} \text { (As } A A^{\prime} \text { is Diameter) }}

Let P(x, y) be a point on the ellipse

Draw PN perpendicular to the major axis and PN to meet the auxiliary circle at Q. 

Let  \mathrm{\angle ACQ} be \theta (This angle is also known as Eccentric Angle). Hence, the parametric equation of circle at point Q (a cosӨ, a sinӨ).

Thus, P  has x-coordinate as a cosӨ

As P lies on the ellipse

\\ {\frac{\mathrm{a}^{2} \cos ^{2} \theta}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{b}^{2}}=1 \Rightarrow \mathrm{y}=\pm \mathrm{b} \sin \theta}\\ \\ {\text { Hence, Point } \mathrm{P} \text { is }(\mathrm{a} \cos \theta, \mathrm{b} \sin \theta)}

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Parametric equation of Ellipse

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Parametric equation of Ellipse Current Topic

Coordinate Axes
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Excenters of Triangle
Circumcentre and Orthocentre
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Area of Triangle in Coordinate Geometry
Locus
Transformations of Axes

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