# What is the equation in standard form of the parabola with a focus at (2,-4) and a directrix of y= 6?

##### 1 Answer

Nov 7, 2016

#### Explanation:

The general form for the equation of a horizontal directrix is

The focus of a parabola with a horizontal directrix is of the general form

Therefore, we can write these 3 equations that will help us:

h = 2

-4 = k + f

6 = k - f

solve the last two equation for k and f:

The vertex form of the equation of this type of parabola is:

Because we are not given the value of a, substitute

Substitute our known values into the above equation:

Expand the square:

Distribute

Combine the constants: