# How do you classify x^2-y^2-4x-3=0?

Jun 22, 2015

It is an equation of a hyperbola

#### Explanation:

The equation contains ${x}^{2}$ and ${y}^{2}$ so it may be:

1. Circle or elypse
2. Hyperbola

But the sign of ${y}^{2}$ is negative, so it cannot be an elipse or circle.

You can also check if it is possible to transform the eqation to form:

${x}^{2} / {a}^{2} - {y}^{2} / {b}^{2} = 1$ $\left(1\right)$

${x}^{2} - {y}^{2} - 4 x - 3 = 0$

${x}^{2} - 4 x \textcolor{red}{+ 4} \textcolor{red}{- 4} - 3 - {y}^{2} = 0$

${\left(x - 2\right)}^{2} - {y}^{2} = 7$

${\left(x - 2\right)}^{2} / 7 - {y}^{2} / 7 = 1$

So this equation is in the form (1) which prooves it is a hyperbola