Question

A point $P$ on an ellipse is at a distance of $6$ units from a focus. The eccentricity of the ellipse is $\frac{3}{5}$, then the distance of $P$ from the corresponding directrix is

• A. $\frac{8}{5}$
• B. $\frac{5}{8}$
• C. $10$
• D. $12$
• E. None of these

Answer 1

The correct option is C

$10$

Finding the distance of p :

Let the focus be F and M be any point on the directrix

By basic definition $PF=ePM$

$\Rightarrow$ $6=\frac{3}{5}PM$

$\Rightarrow$$PM=\frac{30}{3}$

$=10$

$\therefore$the distance of $P$ from directrix is $10$

Hence, Option ‘C’ is Correct.