Hyperbola: Graph from equation: Simple: Find the standard equation and draw the graph for

The form of the standard equation is .

Let's try dividing both sides by 225 and get

. After canceling, we get

. We can also write it this way for emphasis:

.

Now we compare this equation with the general equation to conclude that h and k are both 0, a is 5 and b is 3.

The standard graph has its center at (h, k). Here that is (0, 0), or the origin. The vertices of the hyperbola are "a" units to the right and left of the center, or at x = -5 and x = 5.

The asymptotes go through the center with slopes +b/a and -b/a. In this case the slopes are 3/5 and -3/5.

The foci are +/- c units on either side of the center, where

We can check our results by substituting the x-coordinate of a vertex into the original equation and determining the corresponding y-coordinate. It should agree with the value of k, the y-coordinate of the center and the vertices. Using either x=5 or -5, we get

, or , as we expect.

Draw your graph. When complete, check it.