JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q81

MathematicsSingle correct+4 / -1Question 81 of 90

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 :

\dfrac13

\dfrac1{\sqrt3}

\sqrt3

Answer and worked solution

Official answer: D

Tangent $y=mx+\frac1m$ through $(-2,-1)$ : $2m^2-m-1=0$ , so $m=1$ or $-\frac12$ .
$|\tan\alpha|=\left|\frac{1+\frac12}{1-\frac12}\right|=3.$

JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 81