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
• B. conjugate hyperbola
• C. one of the directrix
• D. one of the asymptotes

Answer 1

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.