Let S be the focus of the parabola y²=8x and let PQ be the common chord of the circle x²+y²-6x-8y=0 and the given parabola. The area of the △PQS is 4576

Given Parabola:⇒y²=8x
Given Circle:(x-3)²+(y-4)²=5⇒
Take a point on the parabola as(2t²,4t)≡(x,y)
Solve equations simultaneously⇒4t⁴+16t²-8t²-56t=0⇒t⁴+3t²-8t=0⇒t(t³+3t-8)=0⇒t=0,1⇒We get the points as P(0,0) and Q(2,4).⇒
The distance between (0,0)≡(x1,y1) and (2,4)≡(x2,y2) is given by,⇒Distance Formula=√(x2-x1)²+(y2-y1)²∴Distance=2√5⇒
Focus of parabola y²=8x has coordinates (2,0).⇒
PQS will form a right-angled triangle with area 1/2 × 2 × 4=4 square units.