If the circle x 2 + y 2 = a 2 intersects the hyperbola xy =…

Maths Conic Sections Hyperbola Single Correct MCQ

Published on: August 14, 2026

If the circle x 2 + y 2 = a 2 intersects the hyperbola xy = c 2 in four points P (x 1 , y 1 ), Q(x 2 , y 2 ) R(x 3 , y 3 ), S(x 4 , y 4 ) then

x 1 + x 2 + x 3 + x 4 = 0

y 1 + y 2 + y 3 + y 4 = 0

x 1 x 2 x 3 x 4 = c 4

y 1 y 2 y 3 y 4 = c 4

Text Solution

Verified by Experts

The correct answer is:

Solving given equation we have x 2 +

⇒ ⇒ x 4 - a 2 x 2 + c 4 = 0.

∴ ∴ Σ Σ x 1 = x 1 + x 2 + x 3 + x 4 = 0 and x 1 x 2 x 3 x 4 = c 4 Replacing x by y, we get Σ Σ y 1 = 0 and y 1 y 2 y 3 y 4 = c

4 .

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