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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
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
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