Question

Find the equation of tangent to the circle $x^2+y^2=4$ and parallel to the line x+2y+3=0.

Answer 1

The tangents to the circle $x^2+y^2=4$ in the slope is given by $y=mx\pm 2\sqrt{1+m^2}$

These will be parallel to the line $x+2y+3=0$

if $m=\frac{-1}{2}=$ slope of the line

Required tangents are $y=\frac{-1}{2}x\pm 2\sqrt{1+\frac{1}{4}}$

$2y+x=\pm 2\sqrt{5}$