Section 8.1 Conic Basics

Names of Conics  Circle  Ellipse  Parabola  Hyperbola

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

General form of a second degree equation in two variables Use the discriminant (B 2 – 4AC) determine the shape of conics. ConicDiscriminant EllipseB 2 – 4AC < 0 ParabolaB 2 – 4AC = 0 HyperbolaB 2 – 4AC > 0

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.

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

Determine the type of Conic Hyperbola