For any real is a point on the hyperbola

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For any real

t, x = 2 + \frac{e^t + e^{-t}}{2}, y = 2 + \frac{e^t - e^{-t}}{2}

is a point on the hyperbola

x^2 - y^2 - 4x + 4y - 1 = 0

. Find the area bounded by the hyperbola and the lines joining the centre to the points corresponding to

t_1

and

-t_1