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### Circle definition

A circle is the set of all points in a plane that are equidistant from a fixed point.

### Parabola definition

A parabola is the set of all points in a plane equidistant from a given point and a given line.

### Parabola equation

opens up/down: y - k = (1 / 4p)(x - h)^2

opens left/right: x - h = (1 / 4p)(x - h)^2

p = distance from vertex to focus

### Ellipse definition

An ellipse is the set of all point in a plane such that the sum of the distance to two fixed points is a constant.

### Ellipse equation

horizontal: [(x - h)^2 / a^2] + [(y - k)^2 / b^2] = 1

Vertical: [(x - h)^2 / b^2] + [(y - k)^2 / a^2] = 1

a^2 - b^2 = c^2

### Hyperbola definition

A hyperbola is the set of all points in a plane such that the difference to two fixed points is a constant.

### Hyperbola equation

left/right: [(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1

Up/down: [(y - k)^2 / a^2] - [(x - h)^2 / b^2] = 1