Question

The distance of the point $'\theta'$on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$from a focus is

• A. $a(e + \cos\theta)$
• B. $a(e - \cos\theta)$
• C. $a(1 + e\cos\theta)$
• D. $a(1 + 2e\cos\theta)$

Answer 1

Answer: (C)

$a(1 + e\cos\theta)$

Answer 2

Focal distance of any point $P(x,y)$ on the ellipse is equal to $SP = a + ex$. Here $x = \cos\theta$.

Hence, $SP = a + ae\cos\theta = a(1 + e\cos\theta)$