PQ and RS are two perpendicular chord of rectangular hyperbola xy=c^2.If C is the centre of the hyperbola,then the product of the slopes ofCP,CQ,CR and CS is equal to

a. -1

b.0

c.-1

d none

Let Point P is (ct1,c/t1)

    Point Q is (ct2,c/t2) 

   Point R is (ct3,c/t3) 

   Point S is (ct4,c/t4) 

slope of chord PQ is = -1/t1t2

slope of chord RS is  = -1/t3t4

both chord are perpendicular so

  -1/t1t2  X -1/t3t4  =-1

or t1t2t3t4 =-1

now slope of CP =1/t1²

now slope of CQ =1/t2²

now slope of CR =1/t3²

now slope of CS =1/t4²

so product of slope =1

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin