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

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Answer 1 · 2015-11-11T14:26:01

hyperbola

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, $(x - 1)^2$ is positive while $(y + 2)^2$ is negative.
Hence, the equation is that of a hyperbola

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