9.2 Ellipses
An ellipse is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points, foci, is constant.
The line through the foci intersects the ellipse at two points called verticies. The chord joining the vertices is the major axis, and its midpoint is the center of the ellipse. The chord perpendicular to the major axis at the center is the minor axis. The standard form of the equation of an ellipse with center (h, k) and major and minor axes of lengths 2a and 2b, respectively, where 0 < b < a, is |
Finding the Standard Equation of an Ellipse
Sketching, Graphing, and Analyzing an Ellipse
Application
Halley's comet has an elliptical orbit with the sun at one focus. The eccentricity of the orbit is approximately 0.97. The length of the major axis of the orbit is about 35.88 astronomical units. (An astronomical unit is about 93 million miles.) Find the standard form of the equation of the orbit. Place the center of the orbit at the origin and place the major axis on the x axis.
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Eccentricity
Eccentricity is used to measure the ovalness of an ellipse. The eccentricity e of an ellipse is given by the ratio e = c/a .
0 < e < 1 for every ellipse, so 0 < c < a. Circles have an eccentricity of 0 .
Eccentricity is used to measure the ovalness of an ellipse. The eccentricity e of an ellipse is given by the ratio e = c/a .
0 < e < 1 for every ellipse, so 0 < c < a. Circles have an eccentricity of 0 .