Question

If equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a rectangular hyperbola, then

• A. $\Delta \ne 0,h^2>ab,a+b=0$
• B. $\Delta \ne 0,h^2<ab,a+b=0$
• C. $\Delta \ne 0,h^2=ab,a+b=0$
• D. $\Delta \ne 0,h^2<ab,a+b\ne 0$

Answer 1

The correct option is A $\Delta \ne 0,h^2>ab,a+b=0$

It is fundamental concept that for equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ to represents a rectangular hyperbola it has to satisfy following condition,
$\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2\ne 0,h^2>ab$ and $a+b=0$