Question

A light ray gets reflected from the $x=-2$, 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. $4x+9y+20=0$
• B. $3y+4x+20=0$
• C. $4y+5x+10=0$
• D. $y+x-7=0$

Answer 1

The correct option is B $3y+4x+20=0$

Any tangent of $x^2+y^2=4$ is $y=mx\pm 2\sqrt{1+m^2}$ if it passes through (-2, -4) then $(2m-4{)}^2=4(1+m^2)$
$\Rightarrow 4m^2+16-16m=4+4m^2$
$\Rightarrow m=\infty ,m=\frac{3}{4}$
Hence, slope of reflected ray is $\frac{3}{4}$.
Thus, equation of incident ray is $(y+4)=-\frac{4}{3}(x+2)$,
i.e., $3y+4x+20=0$