Equations x=acosθ, y=bsinθ (a>b) represent a conic section whose eccentricity e is given by

Question

Equations $x=a \cos \theta, y=b \sin \theta(a>b)$ represent a conic section whose eccentricity $e$ is given by

(a) $e^2=\frac{a^2+b^2}{a^2}$

(b) $e^2=\frac{a^2+b^2}{b^2}$

(c) $e^2=\frac{a^2-b^2}{a^2}$

(d) $e^2=\frac{a^2-b^2}{b^2}$

Answer 1

Here, $\cos \theta=\frac{x}{a}$ and $\sin \theta=\frac{y}{b}$

$\therefore \quad \cos ^2 \theta+\sin ^2 \theta=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\therefore \quad e^2=1-\frac{b^2}{a^2}=\frac{a^2-b^2}{a^2}$

So, The correct option of this question will be (C).