Question

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

Answer 1

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.

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