Question

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

• A. $4x+3y+12=0$
• B. $4x+3y=12$
• C. $3x+4y=16$
• D. $3x+4y+9=0$

Answer 1

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

Given ellipse $:16x^2+25y^2=400$
$16x^2+25(4{)}^2=400$

The co-ordinate of $P=(0,4)$

Foci are $(\pm ae,0)=(\pm 3,0)$
$\because$ ray is eminating from one of the focus hence after reflection it will pass through other focus i.e. $(3,0)$
Therefore, the equation of the reflected ray will be $\frac{x}{3}+\frac{y}{4}=1$ or $4x+3y=12$