Let S be the focus of the parabola y ²=8 x and PQ be the common chord of the circle x ²+ y ²-2 x -4 y=0 and the given parabola. The area of P Q S is

Step-by-step solution

The parametric equations of the parabola y²=8 x are x=2 t² and y=4 t and the given equation of circle is x²+y²-2 x-4 y=0 On putting x=2 t² and y=4 t in circle we get array l 4 t⁴+16 t²-4 t²-16 t=0 4 t²+12 t²-16 t=0 4 t (t³+3 t-4 )=0 t(t-1) (t²+t+4 )=0 t=0, t=1 [ t²+t+4 0 ] array Thus the coordinates of points of intersection of the circle and the parabola are Q (0,0) and P (2,4) . Clearly these are diametrically opposite points on the circle. The coordinates of the focus S of the parabola are (2,0) which lies on th