i cant figure out how to write an equation for parabola with a directrix of x instead of y. it is very confusing please help me !!!!!

## write an equation for a parabola with a focus of (1,1) and a directrix of x=6

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# 1 Answer

write an equation for a parabola with a focus of (1,1) and a directrix of x=6

With a vertical directrix the parabola must be horizontal.

The Axis of Symmetry will be y = 1 because the focus must lie on it.

y = 1 intersects x = 6 at (6,1).

The Vertex will be the midpoint ((1+6)/2,(1+1)/2) = (3.5,1).

p = 1 - 3.5 = -2.5

4p(x-h) = (y-k)^2 becomes 4(-2.5)(x-3.5) = (y-1)^2, or

x = f(y) = –(1/10)(y-1)^2 + 7/2

Here’s a GeoGebra graph: http://www.wyzant.com/resources/files/267121/horizontal_parabola

With a vertical directrix the parabola must be horizontal.

The Axis of Symmetry will be y = 1 because the focus must lie on it.

y = 1 intersects x = 6 at (6,1).

The Vertex will be the midpoint ((1+6)/2,(1+1)/2) = (3.5,1).

p = 1 - 3.5 = -2.5

4p(x-h) = (y-k)^2 becomes 4(-2.5)(x-3.5) = (y-1)^2, or

x = f(y) = –(1/10)(y-1)^2 + 7/2

Here’s a GeoGebra graph: http://www.wyzant.com/resources/files/267121/horizontal_parabola