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In the adjoining, OABO is the region of ...

In the adjoining, `OABO` is the region of the ellipse `9x^(2)+y^(2)=36` which lies in first quadrant. If `OA= 2,OB=6,` then find the area of the region bounded by chord AB and arc AB.

A

`(3pi-8)sq.` units.

B

`(3pi-7)sq.` units.

C

`(3pi-6)sq.` units.

D

`(3pi-9)sq.` units.

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of AB
`y-0=(6-0)/(0-2)(x-2)`
`impliesy= -3x+6`
Required area
`=int_(0)^(2)3sqrt(4-x^(2))dx-int_(0)^(2)(-3x+6)dx`
`=3[(x)/(2)sqrt(4-x^(2))+(4)/(2)"sin"^(-1)(x)/(2)]_(0)^(2)-[(-3x^(2))/(2)+6x]_(0)^(2)`
` = 3[(0+2"sin"^(-1)1)-(0+0)]-[(-6+12)-(0+0)]`
`=(3pi-6)sq.` units.
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