Explanation Calculation: Consider the given equation, 36 x 2 + 9 y 2 + 48 x − 36 y + 43 = 0 . Rewrite the given equation in the standard form as follows: 36 x 2 + 9 y 2 + 48 x − 36 y + 43 = 0 Write original equation 36 x 2 + 48 x + 9 y 2 − 36 y + 43 = 0 36 x 2 + 4 3 x + 9 y 2 − 4 y + 43 = 0 Group terms and factor 36 out from of x -term,factor 9 out from of y -term 36 x 2 + 4 3 x + 4 9 − 16 + 9 y 2 − 4 y + 4 − 36 + 43 = 0 Complete the square Simplify further, 36 x + 2 3 2 + 9 y − 2 2 = 9 Write in completed square form 36 x + 2 3 2 9 + 9 y − 2 2 9 = 1 Divide each side by 9 x − − 2 3 2 1 4 + y − 2 2 1 = 1 Write in standard form The given equation is an equation of an ellipse in which the denominator of the y 2 term is greater than the denominator of the x 2 term, so the major axis is vertical. Note that the standard form of the equation for an ellipse with the vertical major axis is given by the equation, x − h 2 b 2 + y − k 2 a 2 = 1 Where, h , k is the center, a and b are the lengths of semi-major and semi-minor axis, respectively. Now, write the given equation in the standard form as, x − − 2 3 2 1 2 2 + y − 2 2 1 2 = 1 On comparison of the above equation with the standard form, x − h 2 b 2 + y − k 2 a 2 = 1 , it is observed that the center is, h , k = − 2 3 , 2 The value of a is 1 and the value of b is 1 2

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ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.3, Problem 46E

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To calculate: The center, vertices, foci, and eccentricity of the ellipse 36x2+9y2+48x−36y+43=0 and then draw the graph.

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Chapter 6.3, Problem 45E

Chapter 6.3, Problem 47E

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The center, vertices, foci, and eccentricity of the ellipse 36 x 2 + 9 y 2 + 48 x − 36 y + 43 = 0 and then draw the graph.

Solution Summary: The author calculates the center, vertices, foci, and eccentricity of the ellipse and draws the graph.

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To calculate: The center, vertices, foci, and eccentricity of the ellipse 36x2+9y2+48x−36y+43=0 and then draw the graph.

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Chapter 6 Solutions