Review of Chapter 6

Other Notes for Chapter 6
-In this set of notes, we learned how to identify conics without using standard form.
-The equations are in the form of Ax^2 + Bxy + Cy + Dx + Ey + F = 0.
-To find the shape of the graph, you compute B^2 - 4AC.

• If it is a circle, you end up with a negative number, and A=C & B=0.


• If it is an ellipse, you get a negative number, and A does not = C & B does not = 0.


• If it is a parabola, you get 0.


• If it is a hyperbola, you get a positive number.

Example 1: Identify the graph of the equation x^2 - 2xy - y^2 = 4.

-A= 1 B= -2 C= -1

-(-2)^2 - 4(1)(-1) = 4 + 4 = 8

-8 is positive, so the graph is a hyperbola

Example 2: Identify the graph of the equation x^2 - 2xy + 3y^2 - 1 = 0.

-A= 1 B= -2 C= 3

-(-2)^2 - 4(1)(3) = 4 - 12 = -8

--8 is negative, A does not = C, and B does not = 0, so its an ellipse