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

11th Edition

ISBN: 9780136845881

Author: Sullivan

Publisher: VST

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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

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...

Knowledge Booster

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