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 area of the equilateral triangle inscribed in the curve C having one vertex as the vertex of curve C is

Options

A. `772 sqrt3"sq. units"`
B. `776sqrt3"sq. units"`
C. `760sqrt3"sq. units"`
D. `768sqrt3"sq. units"`

Answer

D

Explanation

`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"`