Question

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

• A. $x-k=0$ and $y-h=0$
• B. $x+h=0$ and $y+k=0$
• C. $x-k=0$ and $y+h=0$
• D. $x+h=0$ and $y-h=0$

Answer 1

The correct option is A

$x-k=0$ and $y-h=0$

Given : The hyperbola $xy=hx+ky$

$\Rightarrow x(y-h)=k(y-h)+kh$

$\Rightarrow (x-k)(y-h)=kh$

$\therefore$ Joint equation of asymptotes is $(x-k)(y-h)=0$

Hence, the equation of asymptotes are $x-k=0$ and $y-h=0$