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Eccentric Angle : Ellipse

Equation of t...

Question

Equation of the auxiliary circle of the ellipse
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$ is

A

x^{2} + y^{2} = 9

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B

x^{2} + y^{2} = 18

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C

x^{2} + y^{2} = 12

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D

x^{2} + y^{2} = 30

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Solution

The correct option is B $x^{2} + y^{2} = 18$
Given equation of ellipse is
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$
$a^{2} = 12, b^{2} = 18, a < b$
Equation of auxiliary circle is
$x^{2} + y^{2} = b^{2}$
$\Rightarrow x^{2} + y^{2} = 18$

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Eccentric Angle : Ellipse

Standard XII Mathematics

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