# How do you graph the hyperbola #(x+1)^2/9-(y-3)^2/4=1# and find the center, lines which contain the transverse and conjugate axes, the vertices, the foci and the equations of the asymptotes?

##### 1 Answer

See all the stuff below for an explanation!

#### Explanation:

graph{(((x+1)^2)/9)-(((y-3)^2)/4)=1 [-11.165, 8.835, -2.2, 7.8]}

This is what the graph of your equation looks like. Pretty cool, right? Let's find out how to get this.

First, let's get our center. For this, let's look at the equation we have. The center of a hyperbola will have the opposites of the two numbers after the

We can also find our lines that have the transverse and conjugate axes. Since this is a horizontal hyperbola (

Next, let's find our

Let's plug in our values.

So, we have our values. What next? Let's get our vertices, which are always

The foci are also along the same line, but they are

Finally, let's get the asymptotes. For a horizontal hyperbola, the asymptotes are

So sorry for the long answer, but there was a lot of info to cover. Hope this helps!