Question

Find the angle between the tangents drawn from the origin to the parabola, $y^2=4a(x-a)$.

• A. $\pi /2$
• B. $\pi /3$
• C. $\pi /4$
• D. $\pi /6$

Answer 1

Answer: (A)

$\pi /2$

Given parabola is, $y^2=4a(x-a)$
Vertex is $A(a,0)$ and the directrix is $x-a=-a\Rightarrow x=0$
So the origin will lie on the directrix of the given parabola
and we know that pair of tangent drawn to the parabola from its directrix are mutually perpendicular.