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Alg2 lesson 8-6

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Alg2 lesson 8-6

1. 1. (y – 4)2 = 8(x – 1)8(x – 1) = (y – 4)28x – 8 = (y – 4)28x = (y – 4)2 + 8x = (y – 4)2 + 1 Parabola Opens right Focus: (3, 4)1Vertex: (1, 4) 2 Directrix: x = -112Line of symmetry: y = 4 Length of latus rectum: 8
2. 2. x2 + y2 + 6y + 13 = 40x2 + y2 + 6y + 9 = 27 + 9x2 + (y + 3)2 = 36CircleCenter: (0, -3)Radius: 6
3. 3. x2 + 2y2 = 2x + 7x2 – 2x + 1 + 2y2 =7 + 1(x – 1)2 + 2y2 = 8 8 8 8(x – 1)2 + y2 = 1 8 4ellipseCenter: (1, 0)a=2 2 b=2 Vertices: ( 1+2 2 , 0)c2 = 8 – 4 (1- 2 2 , 0)c2 = 4c=2 Foci: (3, 0), (-1, 0)
4. 4. y2 – 4x2 – 4y – 8x - 16 = 0y2 – 4y + 4 – 4(x2 + 2x + 1) = 16 + 4 - 4(y – 2)2 - 4(x + 1)2 = 16 16 16 16(y – 2)2 - (x + 1)2 = 1 16 4Hyperbola Center: (-1, 2)
5. 5. (y – 2)2 - (x + 1)2 = 1 16 4Center: (-1, 2)a = 4 vertices (-1,3) (-1,1)b=2Asymptotes: y = 2x + 4 y = -2xc2 = 16 + 4c2 = 20c = 20Foci: (-1, 2+ 20) (-1, 2- 20)