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.
$P\left(x, y\right)$ on the ellipse is $= SP= a+ex$
Here $x=a\,cos\, \theta$
$\therefore SP = a+ea\,cos\,\theta$
$= a\left(1+e\, cos\,\theta\right)$