Question

Equation of the rectangular hyperbola whose focus is $(1,-1)$ and the corresponding directrix is $x-y+1=0$ is

• A. $x^{2}-y^{2}=1$
• B. $x y=1$
• C. $2 x y-4 x+4 y+1=0$
• D. $2 x y+4 x-4 y-1=0$

Answer 1

Answer: (C)

Eccentricity of rectangular hyperbola is $\sqrt{2}$.
$\therefore$ Equation of hyperbola is
$\sqrt{(x-1)^{2}+(y+1)^{2}}=\sqrt{2} \frac{|x-y+1|}{\sqrt{1^{2}+(-1)^{2}}}$
or $(x-1)^{2}+(y+1)^{2}=(x-y+1)^{2}$
or $2 x y-4 x+4 y+1=0$