Ellipses Name: ________________ An ellipse is the set of pts for which the sum of the distances to two fixed pts is constant 1. On quadrille paper set up an xy-coordinate system and place foci (pushpins) on the x-axis so that the center of the ellipse will be at the origin. Measure the focal length (in cm). Attach string and draw an ellipse. Find and label the cardinal points. c = _________ N: ___________ 2. S: ___________ E: ___________ W: ___________ Pick any two, non-cardinal points on the ellipse. Measure the distances to the foci. Complete the table below. Point Distance to left focus, in cm. Distance to right focus, in cm Sum of distances N S E W Is there experimental support for the characterization of an ellipse as the set of points for which the sum of the distances to two, fixed pts is constant? 3. Measure a, the length of the semi-major axis, in cm. a =____________ Measure b, the length of the semi-minor axis, in cm. b =____________ The length of the string that you used to draw the ellipse is just 2a. Does the data from 2. and 3. support that? Explain why the length of the string should be 2a – hint : use the E and W cardinal pts. Write the equation of the ellipse that you graphed. The Pythagorean theorem and ellipses On the ellipse that you graphed, identify (perhaps with colored pencils) a right triangle with hypotenuse, a, the length of the semi-major axis, and legs b, the length of the semi-minor axis, and c, the focal length. What exciting relationship exists between these quantities?