Question

If length of focal chord of $y^2=4ax$ is $l$, then angle between axis of parabola and focal chord is

• A. $\pm {\sin }^{-1}\sqrt{\frac{2a}{l}}$
• B. $\pm {\sin }^{-1}\sqrt{\frac{4a}{l}}$
• C. $\pm {\tan }^{-1}\sqrt{\frac{4a}{l}}$
• D. $Noneofthese$

Answer 1

The correct option is B $\pm {\sin }^{-1}\sqrt{\frac{4a}{l}}$

Length of total chord which makes an angle $\theta$

with $xaxis=4a{\csc }^2\theta$

$\Rightarrow 4a{\csc }^2\theta =l$

$\Rightarrow {\csc }^2\theta =\frac{l}{4a}$

$\Rightarrow {\sin }^2\theta =\frac{4a}{l}$

$\Rightarrow \theta =\pm {\sin }^{-1}\sqrt[+]{+\frac{4a}{l}}$