#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 1. The area region bounded by the parabolas y2=4ax and x2=4ay is

Arun
25763 Points
3 years ago
We have, y2 = 4ax --------------------------- (1)
x2 = 4ay ---------------------------- (2)
(1) and (2) intersects hence
x = y2/4a (a > 0)
=> (y2/4a)2 = 4ay
=> y4 = 64a3
=> y4 – 64a3y = 0
=> y[y3 – (4a)3] = 0
=> y = 0, 4a
When y = 0, x = 0 and when y = 4a, x = 4a.
The points of intersection of (1) and (2) are O(0, 0) and A(4a, 4a).
The area of the region between the two curves
= Area of the shaded region
04a(y1 – y2)dx
04a[√(4ax) – x2/4a]dx
= [2√a.(x3/2)/(3/2) – (1/4a)(x3/3)]04a
= 4/3√a(4a)3/2 – (1/12a)(4a)3 – 0
= 32/3a2 – 16/3a2
= 16/3a2 sq. units