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Question

PQ, RS are two perpendicular chords of the hyperbola xy=c2. If T is the centre of hyperbola, then product of the slopes of TP, TQ, TR, TS is

A
-1
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B
1
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C
tending to infinity
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D
0.0
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Solution

The correct option is B 1
Let coordinates of P, Q, R, S be respectively.
(ct1,ct1),(ct2,ct2),(ct3,ct3),(ct4,ct4)PQRS(ct2ct1ct2ct1)(ct4ct3ct4ct3)=1(1t1t2)(1t3t4)=1t1t2t3t4=1
Now product of slopes i.e., 1t21.1t22.1t23.1t24=(1)2=1

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