Question

If the double ordinate of the parabola $y^2=8x$ 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 $AB=2y_1=16$

$A\left(x_1,8\right)$ and $B\left(x_1,-8\right)$
$A$ and $B$ lies on parabola. So,
$64=8x_1$
$\Rightarrow x_1=8$
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 $OA$ )
Angle subtended by double ordinate $AB$ at vertex
$=2\alpha$
$=2\cdot \pi /4=\pi /2$