I think you got it all right, except for the sign of the coefficient of the y squared term. This parabola opens to the left and is in the 2nd and 3rd quadrants. So the sign has to be negative. It's -1/14, not +1/14

A parabola is the collection of all points (x,y) equidistant from a point (the focus) and a line (the directrix).

Let (x,y) be a point on the parabola, any point.

The distance from (x,y) to x=3 is the same as the distance from (x,y) to (-4,0)

Using the definition of a parabola, find an expression for the distance from (x,y) to the direction line

and to the focus point and set them equal

the distance formula for two points is d =( (x-x_{1)}^{2} + (y-y_{1})^{2})^{1/2}

^{ }substituting for the focus = square root of ^{ }(x+4)^{2}+y^{2} set this equal to the distance from (x,y) to the directrix line or square root of (x+4)^{2 }+ y^{2} = 3-x

square both sides to get (x+4)^{2} + y^{2} = 9-6x+x^{2}

expand left side and cancel x^{2} terms

x^{2} + 8x + 16 + y^{2} = x^{2} - 6x + 9

14x=-y^{2}-7 divide by 14 x=-y^{2}/14-1/2 the coefficient of the y^{2} term is -1/14 not +1/14

Other ways to work this, but you got a sign wrong somewhere

Hira S.

Thank You so much! I forgot the p was negative. :O07/17/19