Stitz-Zeager_College_Algebra_e-book

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

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

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern