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The area of the circle x^2+y^2=16exterio...

The area of the circle `x^2+y^2=16`exterior to the parabola `y^2=6x`is(A) `4/3(4pi-sqrt(3))` (B) `4/3(4pi+sqrt(3))`(C) `4/3(8pi-sqrt(3))` (D) `4/3(8pi+sqrt(3))`

Text Solution

Verified by Experts

the given equations is `x^2+y^2=16...(i)`
`y^2=6x.....(ii)`
Area bounded by the circle and parabola
= `[ area(OADO) +area(ADBA)]`
= `2[ int_0^2 sqrt(16x)dx + int_2^4 sqrt(16-x^2)dx]`
`2[sqrt(6) {(x^(3/2) /(3/2))}_0^2 ] + 2[ (x/2)sqrt(16-x^2) + (16/2)sin^-1(x/4)]_2^4`
solve the equation
we get `(4/3)[4pi +sqrt(3)]` units
Area of circle = `pi(r)^2 = pi(4)^2 =16pi`units
Hence
Required area = `16pi -(4/3)[4pi +sqrt(3)]`
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