Notes - Introduction to Conic Sections Do Play Doh Activity slicing cone into different conic sections. (See Calculus in Motion: Conics Definitions and Graphs) Look at Geo Sketchpad simulations for conic sections. Standard Form for Each Equation Circle Parabola (x - h)2 + (y - k)2 = r2 y = a(x - h)2 + k x = a(y - k)2 + h Ellipse Hyperbola (x - h)2 + (y - k)2 = 1 a 2 b 2 (x - h)2 a2 (y - k)2 a2 For all, center is at (h,k) (y - k)2 = 1 b2 (x - h)2 = 1 b2 Identifying Conics To classify a conic from its general equation: The graph of is one of the following. 1. 2. 3. 4. Circle: Parabola: Ellipse: Hyperbola: A=C AC = 0 AC > 0 AC < 0 OR you can complete the square for the x and y terms to determine the standard form of the conic. EX: Classify the graph of each equation. Use the guidelines above OR complete the square.