Question

A ray emanating from the point $(-4,0)$ is incident on the ellipse $9x^2+25y^2=225$ at the point $p$ with ordinate $3$. The equation of the reflected ray after first reflection is

• A. $6x+4y-12=0$
• B. $3x-8y-12=0$
• C. $3x+8y+12=0$
• D. $3x+4y-12=0$

Answer 1

The correct option is D $3x+4y-12=0$

$9x^2+25y^2=225$

$\frac{x^2}{25}+\frac{y^2}{9}=1$

Slope of ray after reflection $=\frac{0-3}{4-0}=\frac{-3}{4}\left(\frac{y_2-y_1}{x_2-x_1}\right)$

equation of reflected ray passing through (0,3) and slope = $\frac{-3}{4}$

$y-y_1=m(x-x_1)$

$y-3=\frac{-3}{4}(x-0)$