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A point P moves such that the sum of the...

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C.
the equation of the curve `C` is

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Verified by Experts

The correct Answer is:
D
`tan 30^(@)=(4t_(1))/(t_(1)^(2))=(4)/(t_(1))`
`"or "(1)/(sqrt3)=(4)/(t_(1))or t_(1)=4sqrt3`

`AB=8t_(1)=32sqrt3`
`"Area of "DeltaOAB=(sqrt3)/(4)xx32sqrt3xx32sqrt3`
`=768sqrt3"sq. units"`
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