# How do you identify the following equation (x-1)^2/9 - (y+2)^2/25 = 1 as a circle, parabola, ellipse or hyperbola?

Nov 11, 2015

hyperbola

#### Explanation:

The equation is that of an ellipse if the sign of both ${x}^{2}$ and ${y}^{2}$ are both positive.

The equation is that of a circle if the sign of both ${x}^{2}$ and ${y}^{2}$ are both positive and the denominator are the same

The equation is that of a parabola if only one of either ${x}^{2}$ or ${y}^{2}$ exists

The equation is that of a hyperbola if ${x}^{2}$ and ${y}^{2}$ have different signs.

In the given, ${\left(x - 1\right)}^{2}$ is positive while ${\left(y + 2\right)}^{2}$ is negative.
Hence, the equation is that of a hyperbola