# How do I graph #16x^2+y^2+32x-18y=119# algebraically?

##### 1 Answer

Get the equation into a familiar form, and then figure out what each number in that equation means.

#### Explanation:

This looks like the equation of a circle. The best way to get these into a graphable form is to play around with the equation and complete squares. Let's first regroup these...

Now take out the factor of 16 in the x "group".

Next, complete the squares

Hmm... this *would* be the equation of a circle, except there's a factor of 16 in front of the x group. That means it must be an ellipse.

An ellipse with center (h, k) and a horizontal axis "a" and vertical axis "b" (regardless of which one is the major axis) is as follows:

So, let's get this formula into that form.

So, this ellipse is going to be centered at (-1, 9). Also, the horizontal axis will have a length of

If you were to graph this by hand, you would draw a dot at (-1, 9), draw a horizontal line extending about 3.67 units on either side of the dot, and a vertical line extending about 4.7 units on either side of the dot. Then, draw an oval connecting the tips of the four lines.

If this doesn't make sense, here's a graph of the ellipse.

graph{16x^2 + y^2+32x-18y =119 [-34.86, 32.84, -8, 25.84]}