Hyperbola

Let a and b be positive real numbers such that a >1 and b<a. Let P be a point in the first quadrant that lies on the hyperbola

x2

a2

−

y2

b2

=1. Suppose the tangent to the hyperbola at P passes through the point (1,0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let Δ denote the area of the triangle formed by the tangent at P, the normal at P and the x -axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?