JEE Advanced 2020 Mathematics question
Let and be positive real numbers such that and . Let be a point in the first quadrant that lies on the hyperbola . Suppose the tangent to the hyperbola at passes through the point , and suppose the normal to the hyperbola at cuts off equal intercepts on the coordinate axes. Let denote the area of the triangle formed by the tangent at , the normal at and the -axis. If denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?
Answer: (A),(D)
Solution
Let . Tangent: ; it passes through , so . The normal makes equal intercepts, so its slope is and the slope of the tangent is : . lies on the hyperbola:
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