Question

Find the area of the region in the first quadrant enclosed by circle x² + y² = 16 and line y = x.

Answer 1

Centre of circle x² + y² = 16 is origin and radius is 4 line y = x passes through origin and cuts the circle at A.

Then solving x² + y² = 16 and y = x

x = 2√2

∴ Coordinate of A(2√2, 2√2), P(4, 0) and B(2√2, 0)

Thus, rquired area = Area AOBA + Area ABPA