Stitz-Zeager_College_Algebra_e-book

Traditionally f t is used for x and g t is used for y

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Unformatted text preview: 12ed2 and whose minor −e axis has length √2ede2 1− – If e = 1, the graph is a parabola whose focal diameter is 2d. – If e > 1, the graph is a hyperbola whose transverse axis has length conjugate axis has length √2ed 1 . e2 − 2ed e2 −1 and whose 11.6 Hooked on Conics Again 11.6.3 839 Exercises 1. Graph the following equations. √ √ (a) x2 + 2xy + y 2 − x 2 + y 2 − 6 = 0 √ √ (b) 7x2 − 4xy 3 + 3y 2 − 2x − 2y 3 − 5 = 0 √ (c) 13x2 − 34xy 3 + 47y 2 − 64 = 0 (d) 8x2 + 12xy + 17y 2 − 20 = 0 2. Graph the following equations. (a) r = 2 1 − cos(θ) (b) r = 3 2 + sin(θ) (c) r = 4 1 + 3 cos(θ) (d) r = 6 3 − cos θ + π 4 cos(θ) − sin(θ) is called a rotation matrix. We’ve seen this matrix sin(θ) cos(θ) most recently in the proof of used in the proof of Theorem 11.9. 3. The matrix A(θ) = (a) Show the matrix from Example 8.3.3 in Section 8.3 is none other than A π 4 . (b) Discuss with your classmates how to use A(θ) to rotate points in the plane. (c) Using the even / odd identities for cosine and sine, show A(θ)−1 = A(−θ). Interpr...
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