# How do you find the standard equation given focus (8,10), and vertex (8,6)?

##### 2 Answers

The focus is above the vertex, therefore, the vertex form of the equation is:

Use the focus to compute

Expand the equation into standard form.

#### Explanation:

The focal distance, f, is the distance form the vertex to the focus:

Compute the value of "a":

The vertex tells us that

Substituting these values into the vertex form:

Expand the square:

Find the distance between vertex and focus. Call that p.

Since it opens upward, p >0. Use (x-h)2 = 4p(y - k).

#### Explanation:

The equation of the parabola that opens up or down and has vertex (h, k) is

where p is the difference between the y-coordinates of the focus and the vertex.

In this example, p = 10 - 6 = 4, and (h, k) = (8, 6). Therefore,

This may have been the form you were seeking.

[If we want this in the "standard form," that usually means solving for the variable that is not squared. Distribute the 16, and add...

]

If you were only interested in the standard form, set a = 1/(4p) and go straight to the vertex form:

a = 1/(4*4) = 1/16. Therefore,

That is,

Use FOIL and distribute if you prefer the form

I will not spoil that fun for you.