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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