Question

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

• A. $3$
• B. $\frac{1}{3}$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $3$

Given parabola is $y^2=4x$

Here $4a=4\Rightarrow a=1$

Equation of pair of tangents drawn from the point $(-2,-1)$ to the parabola is $S{S}_1=T^2$

$\Rightarrow (y^2-4x)[{(-1)}^2-4(-2)]={[y(-1)-2.1(x-2)]}^2\Rightarrow 9(y^2-4x)={(-2x-y+4)}^2\Rightarrow 4x^2-8y^2+4xy+20x-8y+16=0$

Since $\alpha$ is the angle between the tangents

$\therefore \tan \alpha =\left|\frac{2\sqrt{h^2-ab}}{a+b}\right|=\left|\frac{2\sqrt{4-4(-8)}}{4-8}\right|=|-3|=3$