Conics question help please ? (1 Viewer)

[Tesla]

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 .

I can prove the first part of the question but i can't seem to draw out the required diagram of the hyperbola . any help please ?

 

[lolcakes52]

By the way you phrased the question, i think it sounds like R and M are the same point. Is the Question right?

 

[Tesla]

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