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Stitz-Zeager_College_Algebra_e-book

# 3 prove the distributive property of the dot product

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Unformatted text preview: 11.12 the major axis should have length 2ed 1−e2 = (2)(4) 1−(1/3)2 = 9. 11.6 Hooked on Conics Again 837 (3, 0), even though we are not asked to do so. Finally, we know from Theorem 11.12 that the √ 4 length of the minor axis is √2ede2 = √1−(1/3)2 = 6 3 which means the endpoints of the minor 1− √ 12 axis are 3 , ±3 2 . We now have everything we need to graph r = 3−cos(θ) . 2 y 4 3 3 2 2 1 1 −4 −3 −2 −1 −1 1 2 3 −3 −2 −1 −1 4 1 2 3 4 5 6 x −2 −2 −3 −3 x = −12 −4 y = −4 r= 4 1−sin(θ) r= 12 3−cos(θ) 6 3. From r = 1+2 sin(θ) we get e = 2 > 1 so the graph is a hyperbola. Since ed = 6, we get d = 3, and from the form of the equation, we know the directrix is y = 3. This means the transverse axis of the hyperbola lies along the y -axis, so we can ﬁnd the vertices by looking π where the hyperbola intersects the y -axis. We ﬁnd r π = 2 and r 32 = −6. These two 2 points correspond to the rectangular points (0, 2) and (0, 6) which puts the center of the hyperb...
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