Explanation Given: x 2 + y 2 − 2 x + 4 y − 4 = 0 Group the expression involving x , group the expression involving y and put the constant on the right side of the equation. The result is x 2 − 2 x + y 2 + 4 y = 4 Next, complete the square of each expression in parentheses. Remember that any number added on the left side of the equation must be added on the right. x 2 − 2 x + 1 + y 2 + 4 y + 4 = 4 + 1 + 4 ( x − 1 ) 2 + ( y + 2 ) 2 = 9 ( x − 1 ) 2 + ( y + 2 ) 2 = 3 2 This equation is the standard form of the equation of a circle with radius 3 and center ( 1 , − 2 ) . To graph the equation by hand, use the center ( 1 , − 2 ) and the radius 3. To graph the equation using a graphing utility, solve for y . ( y + 2 ) 2 = 3 2 − ( x − 1 ) 2 y + 2 = ± 9 − ( x − 1 ) 2 y = − 2 ± 9 − ( x − 1 ) 2

10th Edition

ISBN: 9780321979070

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 1, Problem 14RE

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To find: Find the center and radius of each circle. Graph each circle by hand. Determine the intercepts of the graph of each circle.

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Chapter 1, Problem 13RE

Chapter 1, Problem 15RE

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Chapter 1 Solutions

Precalculus (10th Edition)

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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Find the center and radius of each circle. Graph each circle by hand. Determine the intercepts of the graph of each circle.

Solution Summary: The author explains how to find the center and radius of a circle, and determine the intercepts of the graph of each circle.

To find: Find the center and radius of each circle. Graph each circle by hand. Determine the intercepts of the graph of each circle.

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Chapter 1 Solutions