Question

What type of conic section is the following equation? x2 + (y - 5)2 = 12

Answer 1

Short answer: It's a circle.
Argument 
A parabola has a power of x on one side of the equal sign.

A circle (like this one) has variables raised to the second degree (x and y). The number in front of x^2 and y^2 is equal, usually 1.

An ellipse has x^2 and y^2 present, the numbers in front of x^2 is different from the number in front of y^2

hyperbola has a minus sign between the x^ and y^2. or between the y^2 and x^2

These are the main characteristics of each. They are not the only ones.