Question

PQ and RS are two perpendicular chords of the rectangular hyperbola xy = c2. If O is the centre of the hyperbola, then the product of the slopes of OP, OQ, OR and OS is equal to-

• A. –1
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (B)

1

Answer 2

Let P, Q, R, S be having parameters t1, t2, t3, t4

PQ is perpendicular to RS

Ž $\left( \frac{\frac{c}{t_{2}}–\frac{c}{t_{1}}}{ct_{2}–ct_{1}} \right)$× $\left( \frac{\frac{c}{t_{3}}–\frac{c}{t_{4}}}{ct_{3} - ct_{4}} \right)$= –1

Ž t1t2 t3 t4 = – 1

Slope of OP = $\frac{1}{t_{1}^{2}}$

\ product of slopes of OP, OQ, OR, OS = $\frac{1}{t_{1}^{2}t_{2}^{2}t_{3}^{2}t_{4}^{2}}$=$\frac{1}{1}$= 1.