The intersecting points of the given curves are obtained by solving the equations x – y = 4 and y2 = 2x for x and y.
We have y2 = 8 + 2y i.e., (y – 4) (y + 2) = 0 which gives y = 4, –2 and x = 8, 2.
Thus, the points of intersection are (8, 4), (2, –2). Hence
