Question

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

• A. $0$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (B)

$\frac{\pi }{2}$

Any line through origin is $y=mx$. Since, it is a tangent to $y^2=4a(x-a)$, it will cut it in two coincident points.
So, roots of $m^2{x}^2-4ax+4a^2=0$ are equal.
Product of slope $=-1$ i.e., $b^2-4ac=0$
$\Rightarrow 16a^2-16a^2{m}^2=0$
$\Rightarrow m^2=1$ or $m=1,-1$
Hence, required angle is right angle i.e., $\frac{\pi }{2}$