I'm having trouble understanding on how to setup an equation for an ellipse. Thanks for any help
DUE: Wednesday, November 20 You may work together with so. How other class members on this project. In fact, I encourage you to do ever, each person must turn in their own project, written up neatly on a separate sheet of paper. Do not ask f or assistance on this project from the Math Center tutors. Show your work to receive credit for these problems. Points will be deducted for sloppy and/or unorganized work. Yo u will also lose points for poor or improper notation. As always, you are more than welcome to come ask me for help. (1) This problem will walk you through a development of the equation of the ellipse with center at e origin (0,0). Recall the definition of the ellipse is the set of points whose sum of distances from two given points (the foci) is a specified constant, say d a) (2 points) If the center of the ellipse is the origin and the ellipse is oriented horizontally, what are the coordinates for the two foci? (Recall the definition of variable c when giving your answer.) b) (6 points) Give the distance from an arbitrary point (x, y) to each of the two foci. NOTE: You will have two different answers. Variables x, y, and c will be used in your answers. c) (2 points) Write an equation for the ellipse using its distance definition. Your answer will contain variables x, y, c, and d. d) (10 points) Use algebraic manipulations to rewrite the equation in our standard form for the ellipse. e) (2 points) Using your answer from (d), find a in terms of c and d D(2 points) Using your answer from (d), find b in terms of c and d g) ( 1 point) Justify the Pythagorean relationship, a2 = b2 + c2 . * This project is continued on the back of this page*
