Question

The angle subtended by double ordinate of length $8a$ at the vertex of the parabola $y^2=4ax$ is

• A. ${45}^o$
• B. ${90}^o$
• C. ${60}^o$
• D. ${30}^o$

Answer 1

The correct option is B ${90}^o$

Let $PQ$ be the coordinate

Hence $P$ has y-coordinate

$=4a$, as $y^2=4ax$

$\Rightarrow$ $x=\frac{y^2}{4a}=\frac{{\left(4a\right)}^2}{4a}=4a$

In $△OMP$

$\tan \theta =\frac{4a}{4a}=1$

$\Rightarrow$ $\theta ={45}^o$

$\Rightarrow$ $\angle POQ=2\theta ={90}^o$