Question

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

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

Answer 1

Answer: (D)

$3$

Given parabola $y^2=4x$
Let the equation of tangent to the parabola be
$y=mx+\frac{1}{m}$
Since, P(-2,-1) lies on this line
$-1=-2m+\frac{1}{m}$
$\Rightarrow 2m^2-m-1=0$
$\Rightarrow m=1,-\frac{1}{2}$
Let $m_1=1$ ,$m_2=-\frac{1}{2}$
Now, $|\tan \alpha |=|\frac{m_1-m_2}{1+m_1{m}_2}|$
$\Rightarrow |\tan \alpha |=3$