(a) Explanation Definition used: Definition 1: “The equation of the hyperbola with center at the origin, vertices ( − a , 0 ) , ( a , 0 ) and foci F 1 ( − c , 0 ) , F 2 ( c , 0 ) is x 2 a 2 − y 2 b 2 = 1 , where c = a 2 + b 2 , a > 0 , b > 0 ”. Definition 2: “The equation of the asymptotes of the hyperbola x 2 a 2 − y 2 b 2 = 1 are y a + x b = 0 and y a − x b = 0 .” Calculation: The given equation of hyperbola is x 2 − 3 y 2 + 12 = 0 . It can be written as follows. y 2 4 − x 2 12 = 12 12 y 2 4 − x 2 12 = 1 Now, compare the equation y 2 4 − x 2 12 = 1 with the hyperbola y 2 a 2 − b 2 b 2 = 1 (b) To determine The length of the transverse axis of the hyperbola y 2 4 − x 2 12 = 1 . (c) To determine To sketch: The graph of the hyperbola y 2 4 − x 2 12 = 1 .

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ISBN: 8220102958371

Author: Watson

Publisher: CENGAGE L

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Chapter 11.3, Problem 24E

(a)

To determine

To find: The vertices, foci and asymptotes of the hyperbola x2−3y2+12=0 .

(b)

To determine

The length of the transverse axis of the hyperbola y24−x212=1 .

(c)

To determine

To sketch: The graph of the hyperbola y24−x212=1 .

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Chapter 11.3, Problem 23E

Chapter 11.3, Problem 25E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 11 Solutions

EBK PRECALCULUS: MATHEMATICS FOR CALCUL

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The vertices, foci and asymptotes of the hyperbola x 2 − 3 y 2 + 12 = 0 .

Solution Summary: The author explains the hyperbola's vertices, foci, and asymptotes.

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To find: The vertices, foci and asymptotes of the hyperbola x2−3y2+12=0 .

The length of the transverse axis of the hyperbola y24−x212=1 .

To sketch: The graph of the hyperbola y24−x212=1 .

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Chapter 11 Solutions