Question

A light ray gets reflected by $y$ -axis. If the point of incidence is $\left(\right.0,-2\left.\right)$ and reflected ray touches the circle $x^{2}+y^{2}-2x-2y+1=0$ , then the equation of incident ray is

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

Answer 1

Answer: (B)

Let $m$ be the slope of the reflected ray $\Rightarrow $ equation of reflected ray is $y+2=mx$
$mx-y-2=0$
touches given circle
$\Rightarrow \frac{\left|\right. m - 1 - 2 \left|\right.}{\sqrt{m^{2} + 1}}=1$
$\Rightarrow m=\frac{4}{3}$
$\Rightarrow $ slope of the incident ray is $-\frac{4}{3}$
$\Rightarrow $ slope of the incident ray is $y+2=\left(- \frac{4}{3}\right)$
$\Rightarrow 4x+3y+6=0$