**Parabolas**

### The equation of a parabola

The equation of a parabola

The parabola is already familiar from previous courses. The graph of a quadratic function is a parabola.

What kind of point set does a parabola describe?

**Example 1**

Find all points equidistant from point *(2,4)* and the line* y = -2.* Let us denote these points *(x, y).*

Distance of point* (x, y)* from point *(2,4)*

The distance of the point *(x, y)* from the line* y = -2.* The standard form of the line* y + 2 = 0*

Set the distances equal and square the equation

Open all parentheses

Simplify and solve for* y*

An equation of a set of points is obtained whose graph is a parabola.

The points of intersection of a parabola and a line, a parabola and a circle, and a parabola and a parabola are also obtained by forming pairs of equations.

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