1026 CHAPTER 10 Analytic Geometry Summary of Conic Sections Equation Graph Description Identification 1 x −h22 =4p1 y −k2 or y −k =a1x −h22, where a = 1 4p x y (h, k) p 0 p F Parabola x =h Graph opens • up if p 701or a 702; • down if p 60 1or a 602. Vertex is 1h, k2. Axis of symmetry is x = h. There is an x2-term. y is not squared. 1 y −k22 =4p1x −h2 or x −h =a1 y −k22, where a = 1 4p x y p p 0 F Parabola y =k (h, k) Graph opens • to the right if p 70 1or a 702; • to the left if p 60 1or a 602. Vertex is 1h, k2. Axis of symmetry is y = k. There is a y2-term. x is not squared. 1x −h22 + 1 y −k22 =r2 x y r 0 (h, k) Circle Center is 1h, k2. Radius is r. x2- and y2-terms have the same positive coefficient. 1x −h22 a2 + 1 y −k22 b2 =1 1a +b2 F9 F x y 0 c b c (h, k) a b a Ellipse Horizontal major axis, length = 2a. c2 = a2 - b2 Center is 1h, k2. x2- and y2-terms have different positive coefficients. 1x −h22 b2 + 1 y −k22 a2 =1 1a +b2 F9 F x y 0 a a c b c b (h, k) Ellipse Vertical major axis, length = 2a. c2 = a2 - b2 Center is 1h, k2. x2- and y2-terms have different positive coefficients. 1x −h22 a2 − 1 y −k22 b2 =1 x a a c c Hyperbola (h, k) F9 F y 0 b b Graph has horizontal transverse axis. c2 = a2 + b2 Asymptotes are y = { b a1x - h2 + k. Center is 1h, k2. x2-term has a positive coefficient. y2-term has a negative coefficient. The following chart summarizes our work with conic sections.
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