10-1 Ellipses Fumbles and Kickoffs

The Definition (Don’t write this down!!) The set of all points in a plane such that the sum of the distances from two fixed points, called foci (plural of focus) is a constant.

The set of all points in a plane such that the sum of the distances from two fixed points, called foci (plural of focus) is a constant. Lets look here

The Picture Is this the fumble or the kickoff? (h,k) axis b major axis minor b Is this the fumble or the kickoff?

The Fumble (h,k) axis b major axis a a minor b

major axis b a (h,k) The Kickoff

So, how are we going to tell which is which? b a a b b a

That’s right!! a > b So, look for the larger number. If it is under x, then it is a fumble. If it is under the y, then it is the kickoff. When graphing, label center, major axis endpoints, minor axis endpoints and foci.

a b a b b a

Where are the foci? What were they? They were part of the original definition The set of all points in a plane such that the sum of the distances from two fixed points, called foci (plural of focus) is a constant.

So where do I put them? They are on the major axis, “c” units from the center. How to find c? Huh? a? b? Where do they come from? OH! The denominators of the standard form of the equation.

Examples Graph the following completely. Remember: Standard Form = 1. How to do this? Pull out any squared term coefficients before completing the square. Then divide so that the entire left side = 1.