Ellipses and Hyperbolas are closely related in both equations and definitions, even though they look nothing alike, so they can be easily learned together. First of all, an ellipse is the set of all points (x, y) the sum of whose distances from two distinct fixed points (foci) is constant. Some terms include: vertices=The line through the foci that intersects the ellipse at two points, major axis=The chord joining the vertices, midpoint=center of the ellipse, minor axis=The chord that is perpendicular to the major axis. Ellipse equations:
The Hyperbola is the set of all points (x, y) the difference of whose distances from two distinct fixed points (foci) is constant. The terms that were defined with the ellipse also apply to hyperbolas. Hyperbola Equations:
As you can see, they are similar in many ways such as how their equations are presented. The main differences that can be confusing and need to be memorized are the differing signs in the equations.
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