Mathematics

Problem

For the hyperbola given by the equation

\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1

, a tangent is drawn at the point

P(4\sec\theta, 3\tan\theta)

. This tangent intersects the asymptotes at points

Q

and

R

. Calculate the area of the triangle

OQR

, where

O

is the origin.