# What is the vertex form of the equation of the parabola with a focus at (6,5) and a directrix of #y=19 #?

##### 1 Answer

Vertex form of the equation of the parabola is

#### Explanation:

Here the directrix is a horizontal line

Since this line is perpendicular to the axis of symmetry, this is a regular parabola, where the

Now the distance of a point on parabola from focus at

Let this point be

Its distance from focus is

Hence,

or

or

As vertex form of equation is

the above is

or

graph{-1/28(x-6)^2+12 [-12.83, 27.17, -2.08, 17.92]}