Question

PSQ is a focal chord of the parabola $y^2=8x$.If SP=6,then write SQ.

Answer 1

The coordinates of the focal chord are $P(a{t}^2,2at)andQ(\frac{a}{t^2},\frac{-2a}{t})$

Comparing $y^2=8xwith{y}^2=4ax$

a=2

Therefore,the coordinates of the focus S is (2,0)

Given: SP=6

$\therefore \sqrt{(2-2t^2)+(4t{)}^2}=6$

$\Rightarrow t^4+2t^2-8=0$

$\Rightarrow t^2=0$

Thus,we have:

$SQ=\sqrt{(2-\frac{2}{t^2})+\left(\frac{4}{t^2}\right)}=\sqrt{(2-\frac{2}{2})+\left(\frac{4}{2}\right)}=3$.