question_answer 1)

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y. 

Answer:

Given curves are       4x2 + 4y2 = 9               ?? (1)       and x2 = 4y                                     ?. (2)                    (1) represents a circle with C = (0, 0) and       For (2), x2 = 4y                   (1) and (2)        4y2 + 16y ? 9 =  0        4y2 ? 2y + 18y ? 9 = 0        2y (2y ? 1) + 9 (2y ? 1) = 0                (2y ? 1) (2y + 9) = 0        y =  by (2)               points of intersection are  and       Required area = shaded area