Question

Two tangents are drawn from the point $(-2,-1)$ to the parabola $y^2=4x$. If $\alpha$ is the angle between those tangents then tan $\alpha$=

• A.
• B.
• C. 2
• D.

Answer 1

The correct option is A

The equation to the pair of tangents is $[-y-2(x-2){]}^2=(1+8\left)\right(y^2-4x)\Rightarrow (-2x-y+4{)}^2=-(y^2-4x)$
$\Rightarrow 4x^2+y^2+16-16x-8y+4xy=9y^2-36x\Rightarrow 4x^2+4xy-8y^2+20x-8y+16=0$
$\therefore tan\alpha =\frac{2\sqrt{4+32}}{|4-8|}=\frac{2\times 6}{4}=3$