Richard T.

Ms. Blackwell's 5th Period

Introductory to College Math

The Ellipse

The earth has an elliptical orbit around the sun (with the sun acting as the center of the earth's orbit). The earth is never more than 10 units from the sun east and west; and 5 units north and south. Use this information to write an equation of an ellipse then graph the ellipse. 

If we allow the sun to be the origin of our graph at (0,0) then we already know the center. We also know that our major axis is 10 units away from the center in each direction (we will allow east and west to be the x-axis and north and south to be the y). This is all the information we need to write our equation.

The definition of an ellipse is:

(x-h)² + (y-k)² = 1                                                                                                                                   a²         b²                                                                                                                 

(h,k) is the center so h=0 and k=0 and a is our major axis and b the minor so a=10 and b=5

  (x-0)² + (y-0)² = 1                                                                                                                                   100         25

This is our equation, now we must graph it. We must have the center, the vertexes and the foci to graph.

We know the center and the vertexes are just the major axis distance plus the x value of our center. So our vertexes are (-10,0) and (10,0).

The equation for foci is big-small^^1/2     big is the larger denominator and small is the smaller denominator. So our focus distance is 75^ ^1/2  = 8.7 You add this to your x value to get the focus point so our focus points are (-8.6,0) and (8.6,0). Now we can graph.         

Character Education Quote:

It's not that I'm so smart, it's just that I stay with problems longer.  ~Albert Einstein

From:http://www.quotegarden.com/perseverance.html

For extra help go to:

http://school.discovery.com/homeworkhelp/webmath/ellipses.html

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