A light ray gets reflected from x = -2. If the reflected ray touches the circle x² + y² = 4 and the point of incident is (-2, -4), then the equation of the incident ray is

Any tangent of x² + y²- 4 is $\mathrm{y}=\mathrm{mx}\pm 2\sqrt{1+{\mathrm{m}}^2}$. If it passes through (-2, -4), then 

$\begin{array}{rl} & (2\mathrm{m}-4{)}^2=4(1+{\mathrm{m}}^2)\\ \mathrm{or} & 4{\mathrm{m}}^2+16-16\mathrm{m}=4+4{\mathrm{m}}^2\\ \mathrm{or} & \mathrm{m}=\mathrm{\infty },\mathrm{m}=\frac{3}{4}\end{array}$

Hence, the slope of the reflected ray is 3/4.

Thus, the equation of the incident ray is 

$(\mathrm{y}+4)=-\frac{3}{4}(\mathrm{x}+2) \text{i.e., }4\mathrm{y}+3\mathrm{x}+22=0.$