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Unformatted text preview: Section 10.4 Rotation of Axes Identifying Conic Sections without Completing the Square Example 2 2 2 2 2 2 2 Identify the graph of each of the nondegerate conic section. a. 4x 8 36 72 4 b. x 2 1 4 20 c. x2y 4 d. x 2 2 x y y x y y y x y + + = + + + = + = + = Rotation of Axes 2 2 Except for degenerate cases, the general seconddegree equation Ax represents one of the conic sections. However, due to the xyterm in the equation, these conic sections are rotated Bxy Cy Dx Ey F + + + + + = in such a way that their axes are no longer parallel to the x and yaxes. To reduce these equations to forms of the conic sections with which you are already familiar, we use a procedure called rotation of axes. Example Write the equation xy=  1 in terms of a rotated x ' ' system if the angle of rotation from the xaxis to the x'axis is 45 . Express the equation in standard form. o y Continued on the next slide Example Use the rotated system to graph xy=  1. Find the vertices on the transverse axis, and the asymptotes....
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 Fall '11
 jayjohn

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