Question

Consider the following figure:

(i) Find the point of Intersection P of the circle x² + y² = 32 and the line y = x.

(ii) Find the area of the shaded region

Answer 1

(i) x² + x² = 32 ⇒ 2x² = 32 ⇒ x² = 16 = 4

Therefore the point of intersection p is (4,4)

(ii) We have x² + y² = 32 ⇒ y = \(\sqrt{32 - x^2}\)

The required area =