Find the area of the circle 4x 2 + 4y 2 = 9 which is interior to the parabola x 2 = 4y
The required area is represented by the shaded area OBCDO.
Solving the given
equation of circle, 4x2 + 4y2 =
9, and parabola, x2 = 4y, we obtain the
point of intersection as
.
It can be observed that the required area is symmetrical about y-axis.
∴ Area OBCDO = 2 × Area OBCO
We draw BM perpendicular to OA.
Therefore, the
coordinates of M are
.
Therefore, Area OBCO = Area OMBCO – Area OMBO
Therefore, the required
area OBCDO is
units