In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact.
Consider a hyperbola whose center is at the origin. A line `x+y=2` touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = `6sqrt2` units.
The angle subtended by AB at the center of the hyperbola is

Options

A. `sin^(-11).(4)/(5)`
B. `sin^(-1).(2)/(5)`
C. `sin^(-1).(3)/(5)`
D. none of these

Answer

C

Explanation

`m_(OA)=-(1)/(2),m_(OB)=-2`
`tan theta=|(-1//2+2)/(1+1)|=(3)/(4)`
`"or "sintheta=(3)/(5)`
`"or "theta=sin^(-1)((3)/(5))`