Explanation Given Information: The equations of the circles are ( x − 4 ) 2 + ( y + 2 ) 2 = 25 and ( x + 1 ) 2 + ( y − 5 ) 2 = 16 . Explanation: The standard form of an equation of a circle with radius r and center ( h , k ) is ( x − h ) 2 + ( y − k ) 2 = r 2 . Compare ( x − 4 ) 2 + ( y + 2 ) 2 = 25 with ( x − h ) 2 + ( y − k ) 2 = r 2 . ⇒ h = 4 , k = − 2 . Thus, the center of the circle ( x − 4 ) 2 + ( y + 2 ) 2 = 25 is ( h , k ) = ( 4 , − 2 ) . Compare ( x + 1 ) 2 + ( y − 5 ) 2 = 16 with ( x − h ) 2 + ( y − k ) 2 = r 2 . ⇒ h = − 1 , k = 5 . Thus, the center of the circle ( x + 1 ) 2 + ( y − 5 ) 2 = 16 is ( h , k ) = ( − 1 , 5 )

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ISBN: 9780136845881

Author: Sullivan

Publisher: VST

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Question

Chapter 1.4, Problem 49AYU

To determine

The equation of the line containing the centers of the circles (x−4)2+(y+2)2=25 and (x+1)2+(y−5)2=16.

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Chapter 1.4, Problem 48AYU

Chapter 1.4, Problem 50AYU

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Chapter 1 Solutions

EBK PEARSON ETEXT PRECALCULUS -- ACCESS

Ch. 1.1 - 1. On a real number line the origin is assigned...Ch. 1.1 - 2. If 3 and 5 are the coordinates of two points on...Ch. 1.1 - 3. If 3 and 4 are the legs of a right triangle,...Ch. 1.1 - 4. Use the converse of the Pythagorean Theorem to...Ch. 1.1 - 5. The area of a triangle whose base is b and...Ch. 1.1 - 6. True or False Two triangles are congruent if...Ch. 1.1 - 7. If ( x,y ) are the coordinates of a point P in...Ch. 1.1 - 8. The coordinate axes divide the xy-plane into...Ch. 1.1 - 9. If three distinct points P , Q and R all lie on...Ch. 1.1 - 10. True or False The distance between two points...

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The equation of the line containing the centers of the circles ( x − 4 ) 2 + ( y + 2 ) 2 = 25 and ( x + 1 ) 2 + ( y − 5 ) 2 = 16 .

Solution Summary: The author explains that the equation of the line 7x+5y=18 contains the centers of a circle with radius r and center

The equation of the line containing the centers of the circles (x−4)2+(y+2)2=25 and (x+1)2+(y−5)2=16.

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Chapter 1 Solutions