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 
. 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 
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?
<e<2
= a 4
= b 4
Text Solution
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(a, d)
As in first quadrant if normal at P is making equal intercepts on axes, then slope of the normal = - 1
slope of tangent =1
equation of tangent at 
and equation of tangent at (x 1 ,y 1 ): 
x 1 = a 2 and 
equation of normal at P: x + y = a 2 + b 2 
B 
(a
2 + b 2 , 0)
Also 
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