Ellipse. Propositions and instructions. Proposition 1
- Alla Stolyarevska
The canonical equation of the ellipse is x² / a² + y² / b² = 1, a>=b. Ellipse x² / a² + y² / b² = 1 can be described by comparing with the circle of radius a centered at the center of the ellipse. For each x such that abs(x)<=a , there are two points E, D on the ellipse, and two points A, C on the circle. The ratio of ordinates of the points E, A and D, C is equal to b/a. The ellipse is obtained from the circle by compressing it to the horizontal axis, the coordinates decrease in the same ratio b/a. Proposition 1 The axes of the canonical coordinate system are the symmetry axes of the ellipse x² / a² + y² / b² = 1, and the origin of the coordinate system is its center of symmetry
Supplementary problems 1) Create point O as intersection of X-axis and Y-axis; 2) Show that the point O is the center of symmetry.