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

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

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