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I still can't picture where the points are on the hyperbola . I just copied the exact question from the Patel textbook .

Show that the gradient of the line joining the points P(ct1, c/t1) and Q(ct2, c/t2) on the hyperbola xy = c2 is -1/t1t2 . The points P, Q, R lie on this hyperbola. The line through P perpendicular to QR meets the line through Q perpendicular to PR at M. Prove that M lies on the hyperbola xy = c2...