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Chapter 10.5 Conic Sections

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Def: The equation of a conic section is given by: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 Where: A, B, C, D, E and F are not all = 0 Identify and Graph 1.) 9x 2 + 16y 2 - 54x + 64y + 1 = 0 (9x 2 - 54x ) + (16y 2 + 64y ) = -1 9(x 2 - 6x ) + 16(y 2 + 4y ) = -1 Group Factor Ellipse Why?

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9(x 2 - 6x ) + 16(y 2 + 4y ) = -1 1.) ( cont.) + 9 + 81 +4 + 64 9(x -3) 2 + 16(y + 2) 2 = 144 Divide by 144 Ellipse Center:(3, -2) Major Axis:(3 ± 4, -2) Minor Axis: (3, -2 ± 3)

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1.) (cont.)

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2.) y 2 - 3x + 6y + 12 = 0 Parabola 3x = y 2 + 6y + 12 Rearrange + 9 3 + Why? Complete the square Vertex: (1, -3) Opens:right Focus: a = so Directrix: 3x = (y 2 + 6y ) + 12

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2.) (cont.)

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3.) x 2 - 8y + y 2 + 11 = 0 Circle Why? x 2 + (y2 - 8y ) = -11+ 16 x 2 + (y - 4) 2 = 5 Center: (0, 4) Radius:

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3.) (cont.) (0, 4)

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Homework Worksheet 7-6

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