JEE Advanced 2022 Mathematics question
Consider the hyperbola
- = 1
with foci at and , where lies on the positive x-axis. Let be a point on the hyperbola, in the first quadrant. Let , with . The straight line passing through the point and having the same slope as that of the tangent at to the hyperbola, intersects the straight line at . Let be the distance of from the straight line , and . Then the greatest integer less than or equal to is .
Answer: 7
Solution
The tangent at bisects . The line through parallel to the tangent meets line (produced beyond ) at , making equal base angles at and ; so triangle is isosceles with , and the distance of from is .
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