Conics - Minor Axis: y axis Minor Axis: x axis Length of...

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The Math Center Valle Verde Tutorial Support Services EPCC 1 Conic Section Formulas Parabola: y = a(x-h) 2 + k x = a(y-k) 2 + h If a > 0, opens up If a > 0, opens right If a < 0, opens down If a < 0, opens left Vertex: (h, k) Vertex: (h, k) Focus: (h, k+p) Focus: (h+p, k) Directrix: y = k-p Directrix: x = h-p Axis of Symmetry: x = h Axis of Symmetry: y = k a = 1 p = 1 4p 4a _______________________________________________________________________ Ellipse: x 2 + y 2 = 1 x 2 + y 2 = 1 a 2 b 2 b 2 a 2 Center: (0, 0) Center: (0, 0) Foci: (c, 0), (-c, 0) Foci: (0, c), (0, -c) Vertices: (a, 0), (-a, 0) Vertices: (0, a), (0, -a) y Intercepts: (0, b), (0, -b) x Intercepts: (b, 0), (-b, 0) Major Axis: x axis Major Axis: y axis
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Unformatted text preview: Minor Axis: y axis Minor Axis: x axis Length of Major Axis: 2a Length of Major Axis: 2a Length of Minor Axis: 2b Length of Minor Axis: 2b c 2 = a 2 – b 2 , a > b > 0 _______________________________________________________________________ Hyperbola: Transverse Axis: Horizontal x 2- y 2 = 1 Center: (0, 0) a 2 b 2 Foci: (c, 0), (-c, 0) V e r t i c e s : ( a , ) , (-a , ) Asymptotes: y = + b X a Transverse Axis: Vertical y 2- x 2 = 1 Center: (0, 0) a 2 b 2 Foci: (0, c), (0, -c) Vertices: (0, a), (0, -a) Asymptotes: y = + a X b c 2 = a 2 + b 2 _______________________________________________________________________ Circle: (x – h) 2 + (y – k) 2 = r 2 Center: (h, k) Radius: r...
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This note was uploaded on 03/01/2012 for the course MATH 141 taught by Professor Nedjlaougouag during the Spring '12 term at City Colleges of Chicago.

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