Question

The curve represented by the equation $xy=1$ represents

• A. a parabola
• B. a circle
• C. a hyperbola
• D. an ellipse

Answer 1

The correct option is C a hyperbola

We have, $xy=1$
On comparing with $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
we have,
$a=0,h=\frac{1}{2},b=0,g=0,f=0,c=-1$
$△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2=\frac{1}{4}\ne 0$
and, $h^2>ab$
$\Rightarrow$ The curve represents a hyperbola.