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JEE Advanced Mathematics question

MathematicsHyperbolaJEE Advanced

The line is tangent to the hyperbola . If this line passes through the point of intersection of the nearest directrix and the -axis then the eccentricity of the hyperbola is

Answer: 2

Solution

The line meets the -axis at , so the directrix is , i.e. .

Condition for to touch the hyperbola: . Here ,

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Question ID VK-110782