Correct Option: A

Given: y² = 4x
x² = 4y

⇒	x4	= 4x
	16

or x⁴ = 64x
or x(x³ – 64) = 0
or x³ = 64
or x = 4
∴ y = 4

∴ Required area = 4∫0		√4x -	x²		dx
			y

=		2 × x3/2 ×	2	-	x³		4
			3		12		0

=	4	× (4)x3/2 -	64
	3		12

=	32	-	16	=	16
	3		3		3

Alternately
For point where both parabolas cut each other
y² = 4x, x² = 4y
∴ x² = 4 √4x
or x² = 8√x
or x⁴ = 16 x
or x³ = 16
∴ x =(4, 0), (–4, 0)
∴ Required area

= 4∫0√4x - 4∫0	x²	dx =		2 ×	2	x3/2 -	x³		4	=	16
	4				3		12		0		3