# Writing the Equation of an Ellipse

Remember the patterns for an ellipse:

(h, k) is the center point, a is the distance from the center to the end of the major axis, and b is the distance from the center to the end of the minor axis.

Remember that

**if the ellipse is horizontal, the larger number will go under the x. If it is vertical, the larger number will go under the y.**

Let's look at a couple examples:

1. Find the equation of this ellipse:

First, let's mark the center point on the graph to make things more clear.

The center point is (1, 2). We can also tell that the ellipse is horizontal. Let's identify a and b. Counting the spaces from the center to the ellipse lengthwise, we can tell that a = 4. Then counting up, we know that b = 2.

Now we need to substitute this information into the pattern. Since it's a horizontal ellipse, we know that the larger number (a) needs to go underneath the x.

Now we need to substitute this information into the pattern. Since it's a horizontal ellipse, we know that the larger number (a) needs to go underneath the x.

Center point: (1, 2) a = 4, b = 2

To finish, we just need to simplify:

2. Find the equation of this ellipse:

Let's mark the center point again to make things more clear.

The center point is (-4, 0). We can also tell that the ellipse is vertical. Let's identify a and b. Counting the spaces from the center to the ellipse vertically, we can tell that a = 6. Then counting to the right, we know that b = 3.

Now we need to substitute this information into the pattern. Since it's a vertical ellipse, we know that the larger number (a) needs to go underneath the y.

Now we need to substitute this information into the pattern. Since it's a vertical ellipse, we know that the larger number (a) needs to go underneath the y.

Center point: (-4, 0) a = 6, b = 3

To finish, we just need to simplify:

**Practice:**Find the equation of each ellipse.

**Answers:**

Related Links:Math Fractions Factors |