The Tilted Ellipse

Strategies and Hints

  1. The ellipses are the same size and shape. One is tilted and the other is not. The major axes are the same length. One is horizontal and one is angled counterclockwise away from the horizontal.

  1. R is the angle used to tilt the ellipse. Using a protractor, students will find it is about 37°. (A computed value for R is 36.87°.)

  1. Using a value of 37°, the tangent of 2R is 3.49.

Solution

R is the angle used to rotate the axes. The quantities A, B, and C are the coefficients of the equation of the ellipse in the x-y coordinate system. A = 34, B = -24, and
C = 41. (The equation of the "untilted" ellipse, the one in the x'-y' coordinate system, is .)