Q. 195.0( 1 Vote )

# Draw a rough sketch of the region {(x, y) : y2 ≤ 6ax and x2 + y2 ≤ 16a2}. Also find the area of the region sketched using method of integration.

Given;

The region {(x, y) : y2 ≤ 6ax and x2 + y2 ≤ 16a2}

By solving the equations: y2 ≤ 6ax and x2 + y2 ≤ 16a2

Through substituting for y2

x2 + 6ax = 16a2

(x − 2a) (x + 8a) = 0

x = 2a.

[as x = -8a is not possible]

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

[By the symmetry of the image w.r.t x axis]

Required area =

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