Question

The asymptotes of the hyperbola xy = hx + ky are ______.

Options

• x – k = 0 and y – h = 0

• x + h = 0 and y + k = 0

• x – k = 0 and y + h = 0

• x + k = 0 and y – h = 0

Answer 1

The asymptotes of the hyperbola xy = hx + ky are x – k = 0 and y – h = 0.

Explanation:

Let, the equation of pair of asymptotes be hx + ky – xy + λ = 0

then, Δ = 0  ...[Δ = abc + 2gfh – af² – bg² – ch²]

⇒ λ = –hk

Now, hx + ky – xy – hk = 0

x(–h + y) – k(y – h) = 0

⇒ (y – h)(x – k) = 0

then, asymptotes are y – h = 0

and x – k = 0