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)PQ⊥RS⇒(ct2−ct1ct2−ct1)(ct4−ct3ct4−ct3)=−1⇒(−1t1t2)(−1t3t4)=−1⇒t1t2t3t4=−1 Now product of slopes i.e., 1t21.1t22.1t23.1t24=(−1)2=1