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Question

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three points out of these lie on a rectangular hyperbola then the fourth point will lie on :

A
the same hyperbola
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B
conjugate hyperbola
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C
one of the directrix
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D
one of the asymptotes
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Solution

The correct option is A the same hyperbola
The points are such that one of the points is the orthocentre of the triangle formed by other three points.
We know that "When a rectangular hyperbola circumscribes a triangle then it also passes through the orthocentre of the triangle"
So, when the vertices of a triangle lie on a rectangular hyperbola the orthocentre also lies on the same hyperbola.

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