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For the hyperbola xy = 8 any tangent of ...

For the hyperbola `xy = 8` any tangent of it at P meets co-ordinates at Q and R then area of triangle CQR where 'C' is centre of the hyperbola is

A

16 sq. units

B

12 sq. units

C

24 sq. units

D

18 sq. units

Text Solution

Verified by Experts

The correct Answer is:
A
Any point of `xy = 8` is `P(sqrt(8)t,(sqrt(8))/(t))`
`:.` Equation of the tangent at P is `(x)/((16t)/(sqrt(8))) + (y)/((16)/(sqrt(8)t)) =1`
`:.` Area of the triangle `=(!)/(2).(16t)/(sqrt(8)). (16)/(sqrt(8)t) =16`
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