Question

Find the area enclosed between the smaller arc of the circle x² + y² – 2x + 4y – 11 = 0 and the parabola y = – x² + 2x + 1 – 2√3.

Answer 1

Given curves are 

x² + y² – 2x + 4y – 11 = 0 

and y = –x² + 2x + 1 – 2√3 

(x – 1)² + (y + 2)² = 16 

and y + 2(√3 – 1) = – (x – 1)² 

Hence, the required area