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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 19 of Exercise 21.3

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19
##### Find the area common to the circle x2 + y2 = 16 a2 and the parabola y2 = 6ax.ORFind the area of the region {(x,y):y2 ≤ 6ax} and {(x,y):x2 + y2 ≤ 16a2}.

To find area given equations are

y2 = 6ax ...(i)

x2 + y2 = 16 a2 ...(ii)

On solving Equation (i) and (ii)

Or x2 + (6ax)2 = 16a2

Or x2 + (6ax)2 – 16a2 = 0

Or (x + 8a) (x – 2a) = 0

Or x = 2a or x = – 8a is not possible solution.

Then y2 = 6a(2a) = 12a2 = 2√3a

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

Equation (ii) represents a with centre (0,0) and meets axes (±4a,0), (0,±4a).

Point of intersection of circle and parabola are (2a,2√3a), (2a, – 2√3a).

These are shown in the graph below: -

Required area = 2[Region ODCO + Region BCDB]

The area common to the circlex2 + y2 = 16 a2 and the parabola y2 = 6ax is

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