Question

If for parabola $y^2=4ax$ half of the length of focal chord is $8a$, then the angle made by focal chord with $x-$ axis is/are

• A. $\frac{\pi }{6}$
• B. $\frac{3\pi }{4}$
• C. $\frac{5\pi }{6}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (A), (C)

$\frac{5\pi }{6}$

Let the angle be $\alpha$, then the length of focal chord is
$4a{\text{cosec}}^2\alpha =2\left(8a\right)\Rightarrow {\text{cosec}}^2\alpha =4\Rightarrow \text{cosec}\alpha =\pm 2\Rightarrow \sin \alpha =\pm \frac{1}{2}\alpha =\frac{\pi }{6},\frac{5\pi }{6}$