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Understanding Conics: Circles, Ellipses, Parabolas, and Hyperbolas

Learn the definitions and general form of conics such as circles, ellipses, parabolas, and hyperbolas. Use the discriminant to determine the shape of conics. Follow steps to identify and calculate the discriminant for different types of conics. Understand how to determine the type of conic based on the equation.

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Understanding Conics: Circles, Ellipses, Parabolas, and Hyperbolas

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  1. Section 8.1 Conic Basics

  2. Names of Conics • Circle • Ellipse • Parabola • Hyperbola

  3. Definitions • Circle • The set of all points, equidistant from the same point • Parabola • The set of all points, equidistant from both a line and a point • Ellipse • The set of all points, the sum of whose distances to two fixed points is constant • Hyperbola • The set of all points, the difference of whose distances to two fixed points is a constant

  4. General form of a second degree equation in two variables Use the discriminant (B2 – 4AC) determine the shape of conics.

  5. Determine the type of conic Step 1: Identify A,B,C,D,E, and F A = 2 , B = 0, C = 1, D = 0, E = 0, F = -4 Step 2: Calculate the discriminant Ellipse Note: If the equation is an ellipse, and A = C, then it is actually a circle.

  6. Determine the type of conic A = 2, B = 0, C = -1, D = 0, E = 0, F = -4 Hyperbola

  7. Determine the type of Conic Hyperbola

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