Two tangents are drawn from a point (-2,-1) to the curve y²=4x. If α is the angle between them, then |tanα| is equal to:

The correct option is D

3
Given parabola
y²=4x
Let the equation of tangent to the parabola be
y=mx+1/m
Since, P(-2,-1) lies on this line
-1=-2m+1/m ⇒2m²-m-1=0 ⇒m=1, -1/2
Let m₁=1, m₂=-1/2
Then tanα=|m₁-m₂|/|1+m₁m₂| =|1-(-1/2)|/|1+(1)(-1/2)| = (3/2)/(1/2) =3