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# 9_3 - Section 9.3 The Ellipse Instructor Ms Hoa...

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Section 9.3: The Ellipse Instructor: Ms. Hoa Nguyen 1 Ellipse Definition Definition of an Ellipse : Given any POSITIVE constant 2 a and two fixed points F 1 , F 2 ( foci ), the set of all points P such that d ( P, F 1 ) + d ( P, F 2 ) = 2 a is called an ellipse . Note: d ( A, B ) denotes the distance from A to B : d ( A, B ) = ( x A - x B ) 2 + ( y A - y B ) 2 . The line containing the foci F 1 , F 2 is called the major axis . The midpoint of the line segment joining the foci is called the center of the ellipse. The line through the center and perpendicular to the major axis is called the minor axis . The 2 points where the ellipse intersects the major axis are the vertices, V 1 , V 2 of the ellipse. 2 Find the Equation of the Ellipse 1

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Case 1: Major axis is the x -axis, and the center is at the origin. An equation of the ellipse whose Major axis is the x -axis. The center is at the origin. The foci are F 1 = ( - c, 0) and F 2 = ( c, 0). The vertices are V 1 = ( - a, 0) and V 2 = ( a, 0).
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9_3 - Section 9.3 The Ellipse Instructor Ms Hoa...

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