Please help me with this question

label Algebra
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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
May 16th, 2015

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.

May 16th, 2015

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May 16th, 2015
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