Explanation Definition used: Definition 1: “The graph of the general equation of shifted conic A x 2 + C y 2 + D x + E y + F = 0 , where A and C are not both 0 is conic or a degenerate conic”. Definition 2: “The graph of the general equation of shifted conic A x 2 + C y 2 + D x + E y + F = 0 , where A and C are not both 0 is a non-degenerate conic. Then it represents (i) A parabola if A or C is 0 . (ii) An ellipse if A and C have the same sign. (iii) A circle if A = C . (iv) A hyperbola if A and C have opposite sign.” Definition 3: “The equation of the shifted hyperbola with center as ( h , k ) and vertical axis (y-axis) axis as transverse axis is ( y − k ) 2 a 2 − ( x − h ) 2 b 2 = 1 , when a > 0 , b > 0 , c 2 = a 2 + b 2 ”. Calculation: The given conic equation is 9 x 2 + 36 = y 2 + 36 x + 6 y . It can be written as follows. 9 x 2 − y 2 − 36 x − 6 y + 36 = 0 . Now, compare the conic 9 x 2 − y 2 − 36 x − 6 y + 36 = 0 with A x 2 + C y 2 + D x + E y + F = 0 . A = 9 , C = − 1 Since, both A , and C not equate to zero and of have opposite signs, by the definition 2 stated above, the given conic may be a hyperbola. Now, to complete the squares, rewrite 9 x 2 + 36 = y 2 + 36 x + 6 y as, 9 x 2 − 36 x − y 2 − 6 y + 36 = 0 9 ( x 2 − 4 x ) − ( y 2 − 6 y ) + 36 = 0 9 ( x 2 − 4 x + 4 − 4 ) − ( y 2 − 6 y + 9 − 9 ) + 36 = 0 9 ( x 2 − 4 x + 4 ) − 36 − ( y 2 − 6 y + 9 ) + 9 + 36 = 0 Simplify further, 9 ( x − 2 )

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Author: Stewart

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Chapter 11.4, Problem 61E

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To graph: The conic 9x2+36=y2+36x+6y by using graphic device.

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Chapter 11.4, Problem 60E

Chapter 11.4, Problem 62E

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Chapter 11 Solutions

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To graph: The conic 9 x 2 + 36 = y 2 + 36 x + 6 y by using graphic device.

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