10.4_bzat4e

10.4_bzat4e - Section 10.4 Rotation of Axes Identifying...

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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. x-2y 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 second-degree equation Ax represents one of the conic sections. However, due to the xy-term 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 y-axes. 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 x-axis 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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10.4_bzat4e - Section 10.4 Rotation of Axes Identifying...

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