A light ray reflected from $x=-2\text{ . If the reflected ray }$$\text{ touches the circle }{x}^2+y^2=4\text{ and the point of incident is }$

$(-2,-4)\text{ , then the equation of incedents ray}$

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

$(2m-4{)}^2=4\left(1+m^2\right)$

$\text{ or }4m^2+16-16m=4+4m^2$

$\text{ or }m=\mathrm{\infty },m=\frac{3}{4}$

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

Thus, the equation of the incident ray is 

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