# How do you graph #12y^2-25x^2=300# and identify the foci and asympototes?

##### 1 Answer

The foci are

The asymptotes are

#### Explanation:

First, we see turn the equation so that it equals one.

You can simplify this to:

Remember that a hyperbolic equation can be in two forms:

Now, a graph of a hyperbola opens to the left and the right when

Also, a graph of a hyperbola opens to up and down when

Because of this, the foci of a hyperbola is

Similarly, the foci of a hyperbola is

The equation for the asymptote of a hyperbola is

Similarly, the equation for the asymptote of a hyperbola is

Since

Therefore, the foci are

The asymptotes are

I have a graph from desmos.com here to visualize it.