Question

A ray emanating from the point $(-3,0)$ is incident on the ellipse $16x^2+25y^2=400$ at the point P with ordinate $4$. Find the equation of the reflected ray after first reflection.

• A. $4x+3y=12$
• B. $3x+4y=12$
• C. $5x+4y=12$
• D. $6x+4x=13$

Answer 1

The correct option is A $4x+3y=12$

For point p, y co-ordinate is 4.
Given ellipse : $16x^2+25y^2=400$
$16x^2+25(4{)}^2=400$
the co-ordinate of P is $(0,4)$
$e^2=1-\frac{16}{25}$
$e^2=\frac{9}{25}$
$e=\frac{3}{5}$
foci is $(ae,0)i.e..(3,0)$
Therefore, the equation of the reflected ray (PS) will be
$\frac{x}{a}+\frac{y}{b}=1$
or
$4x+3y=12$