Question

Find the area of the region lying between the parabolas:

 y² = 4x and x² = 4y

Answer 1

For finding the points of intersection of the two parabolas, we equate the values of y² from their equations.

From the equation x = 4y, y = x²/4

When x = 0, y = 0

When x = 4, y = 4²/4 = 4

∴ the points of intersection are 0(0, 0) and A(4, 4).

Required area = area of the region OBACO = [area of the region ODACO] – [area of the region ODABO]

Now, area of the region ODACO = area under the parabola y² = 4x, i.e. y = 2√x between x = 0 and x = 4