Q. The asymptotes of the hyperbola $xy = hx + ky$ are
A) $x = k,\ y = h$
B) $x = h,\ y = k$
C) $x = h,\ y = h$
D) $x = k,\ y = k$
Explanation
(a)
Given that, $xy = hx + ky$
$\Rightarrow (x - k)(y - h) = hk$
On shifting origin to $(k,\ h)$ the above equation reduces to
$XY = hk = c^{2}$ (say)
Where, $x = X + k$ and $y = Y + h$
Then, the equation of the asymptotes are $X = 0$ and $Y = 0\ ie,\ x = k,\ y = h$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.