Two tangents are drawn from a point (-2,-1) to the curve y^2=4x.

Question

Two tangents are drawn from a point $(-2,-1)$ to the curve $y^2=4x$. If $\alpha$ is the angle between them, then $|	an\alpha|$ is equal to:

Accepted Answer

The locus of the point of intersection of two tangents to $y^2=4ax$ inclined at angle $\alpha$ is $\tan^2\alpha(x+a)^2=y^2-4ax$. Here $a=1$, point $(-2,-1)$:
$$\tan^2\alpha(-2+1)^2=(-1)^2-4(1)(-2)\Rightarrow\tan^2\alpha=1+8=9\Rightarrow|\tan\alpha|=3.$$

Solutions · 1