How do you find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3?

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Answer 1 · 2016-12-09T07:15:36

THe equation of the parabola is #y^2=12x#

The vertex is midway between the focus ad the directrix

So, the vertex is #(0,0)#

Let #P=(x,y)# be a point on the parabola.

The distance of P from the directrix is equal to the distance from the focus.

#x+3=sqrt((x-3)^2+(y-0)^2)#

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

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

#y^2=12x#

graph{y^2=12x [-10, 10, -5, 5]}