11.3 Ellipse

11.3 Ellipse - 11.3: The Ellipse Equations, given center...

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Unformatted text preview: 11.3: The Ellipse Equations, given center (h, k), a = distance from center to vertex, b = distance from center to point on minor axis, c = distance from center to either foci, c 2 = a 2 b 2 , a > b > 0, and major axis equal or parallel to: [1] x-axis ( 29 ( 29 x h y k a b 2 2 2 2 1-- + = [2] y-axis: ( 29 ( 29 x h y k b a 2 2 2 2 1- - + = (Note: If a = b, then F 1 = F 2 and we have a circle.) Find the vertices and foci of each ellipse. Graph each equation. 1. x y 2 2 1 9 4 + = 2. 4y 2 + 16x 2 = 32 Write an equation for each ellipse: 3. Ctr: (0, -3) 4. Ctr: (-2, 2) Find the center, vertices, and foci of each ellipse; graph it. (Hint: define a and b) 5. 9(x - 3) 2 + (y + 2) 2 = 18 6. 5x 2 + 10y 2 + 20x 20y - 10 = 0 7. The arch of a bridge is a semiellipse with a horizontal major axis. The span is 50 feet, and the top is 20 7....
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11.3 Ellipse - 11.3: The Ellipse Equations, given center...

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