Question

Let $S$ be the focus of the parabola $y^2=8xandletPQ$ be the common chord of the circle $x^2+y^2-2x-4y=0$ and the given parabola. The area of the triangle $PQS$ is

Answer 1

Claerly $P(2t^2,4t)$ satisfies the equation of circle,

$x^2+y^2-2x-4y=0$

$\Rightarrow 4t^2+16t^2-4t^2-16t=0$

$\Rightarrow t(t^3+3t-4)=0$

$\Rightarrow t(t-1)(t^2+t+4)=0$

$\to t=0,1$

$i.e.,Pbe(2,4)$

$\text{So,~area of}\Delta PQS=\frac{1}{2}\times 2times4=4units$