 ## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 11 of MCQ

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11
##### The area bounded by the parabola y2 = 4ax and x2 = 4ay is

This problem is the generalized form of question 2.

Let’s proceed to solve it similarly –

We need the bounds, i.e., where the area starts and where it ends. At the points of intersection, both the equations are satisfied.

This means that at points of intersection

y2 = 4ax (from the other equation)

Let us solve this. x4 = 64a3x

x(x3 – 64a3) = 0

x = 0 or x3 = 64a3, i.e, x = 4a

So the points of intersection are (0,0) and (4a,4a)

Now, let’s compute the area.

If we integrate w.r.t x, we’ll have to integrate the space between the two curves from x = 0 to x =4a.

i.e.,     (Ans)

1
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1
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