JEE Advanced 2020 Mathematics question
Let and be positive real numbers. Suppose is an end point of the latus rectum of the parabola , and suppose the ellipse passes through the point . If the tangents to the parabola and the ellipse at the point are perpendicular to each other, then the eccentricity of the ellipse is
Answer: (A)
Solution
Take . Slope of the tangent to the parabola: at . Slope of the tangent to the ellipse: at . Perpendicularity: \dfrac{b^2}{2a^2}$) = -1
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