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Let a and b be positive real numbers s...

Let a and b be positive real numbers such that ` a gt 1 and b lt a ` . Let be a point in the first quadrant that lies on the hyperbola `(x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1` . Suppose the tangent to the hyperbola at P passes through the oint (1,0) and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes . Let `Delta ` denote the area of the triangle formed by the tangent at P , the normal at P and the x - axis . If a denotes the eccentricity of the hyperbola , then which of the following statements is/are TRUE ?

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