Making graphs and using equations of ellipses. An ellipse is the set of all points P in a plane such that the sum of the distance from P to 2 fixed points.

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Presentation transcript:

Making graphs and using equations of ellipses

An ellipse is the set of all points P in a plane such that the sum of the distance from P to 2 fixed points F1 and F2 is constant. The 2 fixed points, F1 and F2, are called the foci. An ellipse has 2 axes. The major axis is the longer axis and passes through the foci. The endpoints of the major axis are the vertices of the ellipse. The minor axis is the shorter axis of the ellipse, and its endpoints are the co-vertices. The major and minor axes are perpendicular and their point of intersection is the center of the ellipse.

Major axis major axis Horizontal vertical

Choose the appropriate standard form- the horizontal axis is longer so it is the major axis Find a and b - a= 2 and b = 1

Vertices- (a,0) and (-a, 0) Foci- (c,0) and (-c, 0) Co-vertices – (0,b) and (0, -b)

Vertices- (0,a) and (0, -a) Foci- (0,c) and (0, -c) Co-vertices – (b,0) and (-b,0)

find the vertices, co-vertices, foci and eccentricity

Major axis major axis Horizontal vertical