The area of triangle formed by the tangents from point (3, 2) to hyperbola  and the chord of contact w.r.t. point (3, 2)

(8)

Hyperbola is  or

Equation of tangent is    (1)

It passes through (3, 2)

Or

Solving we get values of  as  and

Equation of tangent (1) for

Or

On taking  sign point  does not satisfy the equation of tangent therefore rejecting  sign. Hence equation of tangent is     (2)

Now equation of tangent (1) for  is  rejecting (+) sign (since taking (+) sign point  does not satisfy this equation)

Hence, equation of tangent is    (3)

Now equation of chord of contact w.r.t. point  is

Or

Or            (4)

Solving (2) and (4);

Solving (3) and (4);

Now vertices of triangle are

 sq. units