The asymptotes of the hyperbola xy = hx + ky are -

Maths Conic Sections Hyperbola Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

x = k, y = h

x = h, y = k

x = h, y = h

x = k, y = k

Text Solution

Verified by Experts

The correct answer is:

The equations of asymptotes are

xy – hx – ky + λ = 0 … (1)

where λ is a constant and (1) represents a pair of straight line.

Here A = 0, B = 0, C = λ , 2H = 1, 2G = –h and 2F = –k.

Then ABC + 2FGH – AF 2 – BG 2 – CH 2 = 0

⇒ 0 + 2 – 0 – 0 – λ . = 0

⇒ = ⇒ λ = hk

Hence, on putting λ = hk in equation (1), we get

xy – hx – ky + hk = 0

(x – k) (y – h) = 0

Asymptotes are x = k, and y = h.

Hence is the correct answer.

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