Question

A light ray gets reflected from $x=-2$. If the reflected ray touches the circle $x^2+y^2=4$ and point of incident is $(-2,-4)$, then equation of incident ray is

• A. $4y+3x+22=0$
• B. $3y+4x+20=0$
• C. $4y+2x+20=0$
• D. $y+x+6=0$

Answer 1

The correct option is A $4y+3x+22=0$

Let the slope of the reflected ray be m. As it passes through $(-2,-4)$ the equation becomes $mx-y=-2m+4$
The distance of the tangent line from origin is equal to radius .
$\Rightarrow \frac{|2m+4|}{\sqrt{m^2+1}}=2$ [condition for the ray of light touching the circle ]
$\Rightarrow m=\frac{-3}{4}$
Now the equation becomes $y+4=\frac{-3}{4}(x+2)$
$\Rightarrow 4y+3x+22=0$