What is the vertex form of the equation of the parabola with a focus at (6,-13) and a directrix of #y=13 #?

1 Answer
Sep 12, 2017

#y=\frac{1}{-52}(x-6)^2+0#

Explanation:

Given the focus and directrix of a parabola, you can find the parabola's equation with the formula:

#y=\frac{1}{2(b-k)}(x-a)^2+\frac{1}{2}(b+k)#,

where:

#k# is the directrix &

#(a,b)# is the focus


Plugging in the values of those variables gives us:

#y=\frac{1}{2(-13-13)}(x-6)^2+\frac{1}{2}(-13+13)#

Simplifying gives us:

#y=\frac{1}{-52}(x-6)^2+0#