Question

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

• A. ${90}^0$
• B. ${30}^0$
• C. ${\tan }^{-1}\left(2\right)$
• D. ${45}^0$

Answer 1

The correct option is A ${90}^0$

Equation of tangent to the parabola, $y^2=4a(x-a)$ with slope $m$ is
given by, $y=m(x-a)+\frac{a}{m}$
Given it passes through $(0,0)$
$\Rightarrow 0=-am+\frac{a}{m}\Rightarrow m=\pm 1$
$m_1=1,m_2=-1\Rightarrow m_1.m_2=-1$
Hence tangent drawn from origin to the given parabola are perpendicular to each other.