Post1330_section8o0 - Chapter 8 Systems: Identify...

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Chapter 8 – Systems 1 Chapter 8 Systems: Identify Equations, Point of Intersection of Equations Classification of Second Degree Equations When you write a conic section in its general form, you have an equation of the form 0 2 2 = + + + + + F Ey Dx Cy Bxy Ax . (All of the equations we have seen so far have a value for B that is 0.) With only minimal work, you can determine if an equation in this form is a circle, an ellipse, a parabola or a hyperbola. If A, B and C are not all 0, and if the graph if not degenerate (point, line or two lines), then: The graph is a circle if 0 4 2 < - AC B and C A = . The graph is an ellipse if 0 4 2 < - AC B and C A . The graph is a parabola if 0 4 2 = - AC B . The graph is a hyperbola if 0 4 2 - AC B . Remember, if there is no “xy” term, then B = 0. Recall the following equations: Parabola: 2 ( ) 4 ( ) y k p x h - = - or 2 ( ) 4 ( ) x h p y k - = - . Circle:
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.

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Post1330_section8o0 - Chapter 8 Systems: Identify...

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