Question

Let the equations of tangents to parabola $y^2=4ax$ which are drawn from the point $(2a,3a)$ be $kx+my+4a=0;px-hy+a=0$ .Find $|k+m+p+h|$?

Answer 1

Any tangent to parabola is given by, $y=mx+\frac{a}{m}$
Given it passes through $(2a,3a)\Rightarrow 3a=2am+\frac{a}{m}$
$\Rightarrow 2m^2-3m+1=0\Rightarrow m=1,\frac{1}{2}$
Hence tangents are $x-y+a=0,x-2y+4a=0$