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Published byBrett Matthews Modified over 8 years ago
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a b Center at( h,k ) An ellipse with major axis parallel to x -axis c Definition
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Important Idea a>ba>b a b ( h,k ) c
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Definition The standard form of the equation of an ellipse when the major axis is parallel to the x -axis
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An ellipse with major axis parallel to y -axis a b Center: at ( h,k ) c Definition
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The standard form of the equation of an ellipse when the major axis is parallel to the y -axis
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Important Idea The direction of the major axis is determined by the larger denominator. The larger denominator is always a 2 in the standard equation. If the larger denominator is under the x term, the ellipse is “fat”; if the larger denominator is under the y term, the ellipse is “skinny”
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Try This For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.
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Solution Center:(0,-4) Foci: Vertices: (±6,-4) Minor Axes Ends(0,1),(0,-9)
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Try This Write an equation of the ellipse with Foci (3,2) and (3,-4) and whose major axes is 14 units long.
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Solution
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How is the “roundness” of an ellipse measured?
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Try This For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.
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Solution Center:(3,2) Foci: Vertices: (-2,2) (8,2) Minor Axes Ends(3,3),(3,1)
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Another For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.
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Solution Center:(2,-3) Foci: Vertices: (6,-3) (-2,-3) Minor Axes Ends(2,-6),(2,0)
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