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
Use the discriminant (B2 – 4AC) determine the shape of conics.
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
Note: If the equation is an ellipse, and A = C, then it is actually a circle.
A = 2, B = 0, C = -1, D = 0, E = 0, F = -4