# Finding and Graphing the Foci of a Hyperbola

Here's an example of a hyperbola with the foci (foci is the plural of focus) graphed:

**The distance from the center point to one focus is called c and can be found using this formula:**

**c**

^{2}= a^{2}+ b^{2}Let's find c and graph the foci for a couple hyperbolas:

This hyperbola has already been graphed and its center point is marked:

We need to use the formula c

We need to use the formula c

^{2}= a^{2}+ b^{2}to find c. Now, we could find a and b and then substitute, but remember that in the pattern, the denominators are a^{2}and b^{2}, so we can substitute those right into the formula:
c

c

c

c = 5

We can plot the foci by counting 5 spaces from the ^{2}= a^{2}+ b^{2}c

^{2}= 9 + 16c

^{2}= 25 We'll need to take the square root.c = 5

**center.**Note that we are not counting 5 spaces from the vertex. Since the hyperbola is horizontal, we will count 5 spaces left and right and plot the foci there.
This hyperbola has already been graphed and its center point is marked:

We need to use the formula c

We need to use the formula c

^{2}=a^{2}+b^{2}to find c. Since in the pattern the denominators are a^{2}and b^{2}, we can substitute those right into the formula:
c

c

c

c ≈ 3.6

We can plot the foci by counting about 3.6 spaces from the ^{2}= a^{2}+ b^{2}c

^{2}= 4 + 9c

^{2}= 13 We'll need to take the square root.c ≈ 3.6

**center.**We'll have to estimate somewhat, but we can be fairly accurate.Since the hyperbola is vertical, we will count 3.6 spaces up and down and plot the foci there.**Practice:**