Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3. serious answers only

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asked Jul 9, 2019 52.8k views

2 Answers

Badgerr · Answer 1 · 2019-07-15T08:50:16+0000

That's a sideways one; let's go back to first principals.

A parabola is the locus of points equidistant from a point called the focus and a line called the directrix.

It's almost always better to work with squared distance:

The squared distance from (x,y) to (3,0) is
(x-3)^2 + y^2

The squared distance from (x,y) to x=-3 is
(x- - 3)^2

Equating,

(x-3)^2 + y^2 = (x+3)^2

x^2 - 6x + 9 + y^2 = x^2 + 6x + 9

y^2 = 12x

x = (1)/(12) y^2