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The tangent and normal to the ellipse 3x...

The tangent and normal to the ellipse `3x^(2) + 5y^(2) = 32` at the point `P(2, 2) `meet the` x`-axis at `Q `and` R`, respectively. Then the area (in sq. units) of the triangle PQR is:

A

`(34)/(15)`

B

`(16)/(3)`

C

`(68)/(15)`

D

`(14)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`3x^(2) + 5y^(2) = 32`
Tangent : `3x + 5y = 16 :. Q ((16)/(3), 0)`
Normal : `y -2 = (5)/(3) (x-2) rArr 5x - 3y -4 = 0 :. R ((4)/(5), 0)`
`Ar DeltaPQR = (1)/(2) |(2,2,1),((16)/(3),0,1),((4)/(5),0,1)|= (68)/(15)`
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