# How do I graph #(y+3)^2/25-(x+2)^2/16=1# algebraically?

##### 1 Answer

This is the equation of a **hyperbola**.

To graph it, you need to interpret your equation to see what goes where.

So the standard hyperbola equations are:

#(x-h)^2/a^2 - (y-k)^2/b^2 = 1# #(y-k)^2/a^2 - (x-h)^2/b^2 = 1#

Equation 1 represents a **horizontal hyperbola** (which looks like this):

Equation 2 Represents a **vertical hyperbola** (shown below):

So first up, we will need to decide which one we have in the given example.

The given equation is:

Since the *y* is the first term, we know that this hyperbola is a **vertical hyperbola**.

Now there are two things we need to find in order to graph:

- The
**center**of the hyperbola. - How far
**up & down**the branches are.

To find the center, all we need to know is that in any hyperbola equation, the **left/right** and **up/down** the hyperbola has translated.

Therefore, the coordinate

So in our equation,

- It's not just 2 because remember, it's
#(x-h)#

Also,

- Once again, be sure that you've got your signs right.

Therefore, the center is **(-2, -3)**

Now for how far up/down, we simply need to understand the following:

#a# represents how far**left and right**the**vertices**of the branches are located.#b# represents how far**up and down**the**vertices**of the branches are located.

The vertices are simply the points where the branches of the hyperbola begin to curve (refer to image below):

Because our hyperbola is **vertical**, we only need to look **up and down** , and hence need only the **b value.**

BE CAREFUL HERE:

What is located in the equation is

Therefore we will need to **square root** it before we can use it.

In this equation,

Now we add these onto the

Final answers:

Center: **(-2, -3)**

Vertices: **(-2, 2)** and **(-2, -8)**

Draw your branches using these and you will be good :)