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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



d none

6 years ago


Answers : (1)


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

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