Question

If $PSQ$ is the focal chord of the parabola $y^2 = 8x$ such that $ SP = 6$ then the length $SQ $ is

• A. 6
• B. 4
• C. 3
• D. none of these.

Answer 1

The Correct Option is C

Latus Rectum $= 4a = 8 $ [Given Parabola is $y^2 = 8x$] $\therefore l=$ Semi-latus rectum $= 4\quad$[General] Parabola is $y^2= 4ax$ $\therefore 4a = 8]$ Since $\frac{2}{l}= \frac{1}{SP}+\frac{1}{SQ}$ $\therefore \frac{2}{4} = \frac{1}{6}+\frac{1}{SQ}$ $ \therefore \frac{1}{SQ} = \frac{1}{2}-\frac{1}{6} $ $ =\frac{ 3-1}{6} = \frac{2}{6}= \frac{1}{3}$ $ \therefore SQ=3$