Section 8.1

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# Section 8.1 - PowerPoint PPT Presentation

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

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### 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 (B2 – 4AC) determine the shape of conics.

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