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 $3$

Since the semi latus rectum of a parabola is the harmonic mean between the segment of any focal chord of a parabola, therefore,$SP,4,SQ$ are in H.P.

$\Rightarrow 4=2\frac{SP.SQ}{SP+SQ}\Rightarrow 4=2.\frac{6.SQ}{6+SQ}\Rightarrow SQ=3$