PC.CS.1.5: Given the equation 𝑎𝑥^2 + 𝑏𝑦^2 + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0, determine if the equation represents a circle, ellipse, parabola, or hyperbola.

Given the equation 𝑎𝑥^2 + 𝑏𝑦^2 + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0, determine if the equation represents a circle, ellipse, parabola, or hyperbola.

Example Problems

A certain circle can be represented by the following equation.

x^2 + 2x + y^2 - 18y + 66 = 0

What is the center of this circle?

A certain circle can be represented by the following equation.

x^2 + y^2 - 121 = 0

What is the center of this circle?

A certain circle can be represented by the following equation.

x^2 + 12x + y^2 + 18 = 0

What is the center of this circle?

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