Question

If the double ordinate of the parabola $y^{2}=8 x$ is of length $16$, then the angle subtended by it at the vertex of the parabola is

• A. $\frac{\pi}{2}$
• B. $\frac{\pi}{3}$
• C. $\frac{3 \pi}{4}$
• D. $\frac{\pi}{4}$

Answer 1

Answer: (A)

Let $A\left(x_{1},\, y_{1}\right)$ and $B\left(x_{1},\,-y_{1}\right)$ are the co-ordinate of end points of double ordinate length of $A B=2 y_{1}=16$

$A\left(x_{1}, 8\right)$ and $B\left(x_{1},-8\right)$
$A$ and $B$ lies on parabola. So,
$64=8 x_{1} $
$\Rightarrow x_{1}=8$
So, coordinate of $A$ and $B$ are $(8,8),(8,-8)$
$\Rightarrow \tan \alpha=\frac{8}{8}=1$
$\alpha=\frac{\pi}{4} ($ Angle with $X$ -axis made by $O A$ )
Angle subtended by double ordinate $A B$ at vertex
$=2 \alpha $
$=2 \cdot \pi / 4=\pi / 2$