First slide

Hyperbola in conic sections

Question

The asymptotes of $x y = h x$ + ky are

Moderate

A

$x = h, y = k$
B

$x = - h, y = - k$
C

$x = k, y = h$
D

$x = - k, y = - h$

Solution

Equation of the asymptotes differ from the equation of the hyperbola by a constant so the equation of the asymptotes is $x y - h x - k y + λ = 0$ which represents a pair of lines if $λ = h k$ and the required asymptotes are $x = k and y = h$ .

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