A family of curves called hyperbolas (discussed in Section 10.4) has the parametric equations x = a tan t, y = b sec t, for -π < t < π and |t| ≠ π/2, where a and b are nonzero real numbers. Graph the hyperbola with a = b = 1. Indicate clearly the direction in which the curve is generated as t increases from t = -π to t = π.