JEE Advanced Mathematics question
Let there be two parabolas with the same axis, focus of each being exterior to the other and the latus recta being and . The locus of the middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a
Answer: (A),(B)
Solution
Two parabolas with a common axis opening the same way cannot each have its focus outside the other, so they open in opposite directions. With the axis as -axis and the origin midway between the vertices, take
= 4a(x - k), = -4b(x + k).
*(Figure: the first parabola opening right with vertex , the
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