Question

Distance SP of a point P on the parabola $y^2=12x$ from its focus S id 6 units. Find the coordinates of the point P.

Answer 1

Given $4a=12\Rightarrow a=3$

$\therefore$focus $=S=(3,0)$

Let we take parametric coordinates of the point P as $(3t^2,6t)$

Given SP=6

$\Rightarrow {(3t^2-3)}^2+36t^2=36$

$\Rightarrow t^4+2t^2-3=0$

$\Rightarrow (t^2-1)(t^3+3)=0$

$\Rightarrow t^2=1$

$\Rightarrow t=\pm 1$

$\Rightarrow$coordinates of point P $=(3,6)$ or $(3,-6)$