To find area enclosed by

Y² = 4ax

...(i)

And X² = 4by

...(ii)

On solving the equation (i) and (ii),

Or, x⁴ – 64ab²x = 0

Or, x(x³ – 64ab²) = 0

Or, x = 0 and x =

Then y = 0 and y =

Equation (i) represents a parabola with vertex (0,0) and axis as x–axis,

Equation (ii) represents a parabola with vertex (0,0) and axis as x - axis,

Points of intersection of parabolas are O (0,0) and

These are shown in the graph below: -

The shaded region is required area, and it is sliced into rectangles of width and length (y¹ – y²)ΔX.

This approximation rectangle slides from x = 0 to , so

Required area = Region OQCPO

The area included between the parabolasy² = 4ax and x² = 4by is