Eccentricity Notes.

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Eccentricity Notes

Eccentricity – The ratio of distances. It basically tells how close a conic section is to being a circle.

Eccentricity In a parabola: e = 1 In an ellipse or hyperbola: The ratio between the foci and the vertices c : a c represents the foci, and a represents the vertices. The more circular the ellipse, the closer the eccentricity is to 0. The eccentricity of an ellipse is always between 0 and 1. The eccentricity of a hyperbola is always greater than 1 In a circle: e = 0

Finding eccentricity: Step 1: Determine what type of conic section the equation is (if there is a number in front of the squared term divide) Step 2: If the conic section is a parabola (e = 1), and if the conic section is a circle (e = 0) Step 3: If the conic section is a hyperbola, or an ellipse then identify the a and c values. Step 4: the eccentricity is the ratio c : a

Find the eccentricity of the conic section represented by the equation.

Find the eccentricity of the conic section represented by the equation.

Find the eccentricity of the conic section represented by the equation.

Write an equation of a hyperbola with center (-2, 6), vertex (6, 6), and e = 2.

Write the equation of a hyperbola with foci at (-1, 7), and (-1, 1) and e = 3.

Write an equation of an ellipse with a center at (3, 4) and a vertex at (3, 9).

Write an equation of an ellipse with foci at (-2, 5), (5, 5).

Homework: P 666 1-12