PGT Mathematics Solution

Find PGT Mathematics Solution of the problem

Solution :

Focus of the parabola \[y^2\ \ =4ax\] is S(a, 0).
Let P(a, 2a) and Q(a, -2a)

\[SP\ =\sqrt{\left(a-a\right)^2+\left(2a-0\right)^2},\ SQ=\sqrt{\left(a-a\right)^2+\left(0+2a\right)^2}\]SP=2a,SQ=2a
\[\frac{2SP\ast S Q}{SP+SQ}=\frac{2\ast2a\ast2a}{2a+2a}=2a\]
Correct option is (2)