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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 9 of Exercise 21.3

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##### Find the area of the region {(x, y) : y2≤8x, x2 + y2≤ 9}

To find area {(x, y): y2 8x, x2 + y29}

y2 = 8x ...(i)

x2 + y2 = 9 ...(ii)

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

Or, x2 + 8x = 9

Or, x2 + 8x – 9 = 0

Or, (x + 9)(x – 1) = 0

Or, x = – 9 or x = 1

And when x = 1 then y = ±2√2

Equation (i) represents a parabola with vertex (0,0) and axis as x – axis, equation (ii) represents a circle with centre (0,0) and radius 3 units, so it meets area at (±3, 0), (0,±3).

Point of intersection of parabola and circle is (1,2√2) and (1, – 2√2).

The sketch of the curves is as below:

Or, required area = 2(region ODCO + region DBCD)

Hence, the required area is sq. units.

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