Question

Sketch the region common to the circle x² + y² = 16 and the parabola x² = 6y. Also, find the area of the region, using integration.

Answer 1

Here x² = 6y is a upward parabola having vertex (0, 0) and x² + y² = 16 is a circle with (0, 0) as centre and 4 as radius.

So the given curve are

x² + y² = 16 …. (1)

x² = 6y ….. (2)

Now by solving both the equations we get A (- 2 √3, 2) and B (2 √3, 2) as the points

So the required area can be written as

Required area = 2 (area of OBCO)

Here

= 2 (area of ODBCO – area of ODBO)