## Description

Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line.

*F*(–2, 0);

*x*= 2

## Explanation & Answer

For the point (x, y) the distance from F is sqrt((x+2)^2 + y^2), from the line x=2 is |x-2|. They have to be equal.

Raise the equation to the second degree:

(x+2)^2 + y^2 = |x-2|^2 = (x-2)^2 and open brackets:

x^2 + 4x + 4 + y^2 = x^2 - 4x + 4,

4x + y^2 = -4x,

**x = -y^2/8**.