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Q.24 The normals at three points P, Q, R on a rectangular hyperbola xy = c2 intersect at a point on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

Q.24 The normals at three points P, Q, R on a rectangular hyperbola xy = c2 intersect at a point on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

Take this hint:

Since the equation of the normal at (ct1, c/t1) to the hyperbola xy = c2is

                          

                         Rectangular Hyperbola

 

Rectangular Hyperbola

 

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Sagar Singh

B.Tech, IIT Delhi

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