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?
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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