Stitz-Zeager_College_Algebra_e-book

In this case k k so k v k v kv w since

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: we have by looking at a special, familiar combination of the coefficients of the quadratic terms. We have the following theorem. Theorem 11.11. Suppose the equation Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0 describes a nondegenerate conic section.a • If B 2 − 4AC > 0 then the graph of the equation is a hyperbola. • If B 2 − 4AC = 0 then the graph of the equation is a parabola. • If B 2 − 4AC < 0 then the graph of the equation is an ellipse or circle. a Recall that this means its graph is either a circle, parabola, ellipse or hyperbola. See page 399. As you may expect, the quantity B 2 − 4AC mentioned in Theorem 11.11 is called the discriminant of the conic section. While we will not attempt to explain the deep Mathematics which produces this ‘coincidence’, we will at least work through the proof of Theorem 11.11 mechanically to show that it is true.5 First note that if the coefficient B = 0 in the equation Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0, Theorem 11.11 reduces to the result presented in Exercise 10 in Sec...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online