10.2: Ellipses

Here is a visual representation of an ellipse and it's components. 

Center

The center is (h,k) 

Foci

The foci are points on the major axis that are in between the vertecies and the center. 

Use these equations to find the foci. 

If the major axis of the ellipse is the x axis, then the ellipse is horizontal. In this case, use this equation: 

If the major axis of the ellipse is the y axis, then the ellipse is vertical. In this case, use this equation:

To find what a and b are and to determine if the ellipse is horizontal or vertical, use this rule:

Another way to find the foci if you know a and b is to use this equation: 

Once you find c, you can use it and the center to find the foci. 

If it is horizontal, the y's will stay constant, so add c to x1 and subtract c from x2 to get your foci. 

Vertex

To find the vertecies, you use a and b. 

if the ellipse is horizontal...

add b to the x value of the center point to find the x value of the first vertex. Likewise, add a to the y value of the center point to find the y value of the second vertex. 

Subtract b from the x value of the center point to find the x value of the second vertex. Likewise, subtract a from the y value of the center point to find the y value of the second vertex. 

If the ellipse is vertical...

Add a to the x value of the center point to find the x value of the first vertex. Likewise, add a to the y value of the center point to find the y value of the second vertex. 

Subtract a from the x value of the center point to find the x value of the second vertex. Likewise, subtract b from the y value of the center point to find the y value of the second vertex. 

Eccentricity of an ellipse

The eccentricity of an ellipse is "the ovalness of the ellipse."

You can find the eccentricity by using this formula:

e=c/a

Math joke of the day:

Q: What should you do when it rains? 

A: Coincide