Explanation Given: Equation of the circle x ² + y ² − x + 2 y + 1 = 0 Calculation:- x ² + y ² − x + 2 y + 1 = 0 ( x ² − x ) + ( y ² + 2 y ) + 1 = 0 ( x ² − x ) + ( y ² + 2 y ) + 1 − 1 = 0 − 1 Subtract 1 from both sides ( x ² − x + 1 4 ) + ( y ² + 2 y + 1 ) = − 1 + 1 + 1 4 Complete the square of each expression in parenthesis ( x − 1 2 ) ² + ( y + 1 ) ² = ( 1 2 ) ² Compare this equation with the equation ( x − h ) ² + ( y − k ) ² = r ² . The comparison yields the information about the circle. We see that h = 1 2 , k = − 1 and r = 1 2 . The circle has centre ( 1 2 , − 1 ) and a radius 1 2 units. To graph the circle, first plot the centre ( 1 2 , − 1 ) . Since the radius is 1 2 units, locate four points on the circle by plotting 1 2 units to the left, to the right, up and down from the centre. These four points can be used to sketch the graph. To find the x -intercepts , if any, let y = 0 and solve for x ...

Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

10th Edition

ISBN: 9780321978981

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 1.4, Problem 31AYU

To determine

To find:

a. The centre $(h, k)$ and radius of the circle $x ² + y ² - x + 2 y + 1 = 0$

b. The graph of the circle

c. Intercepts of the circle, if any

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Chapter 1.4, Problem 30AYU

Chapter 1.4, Problem 32AYU

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Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

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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a. The centre ( h , k ) and radius of the circle x ² + y ² − x + 2 y + 1 = 0 b. The graph of the circle c. Intercepts of the circle, if any

To find: a. The centre ( h, k ) and radius of the circle x² + y² − x + 2y + 1 = 0 b. The graph of the circle c. Intercepts of the circle, if any

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Chapter 1 Solutions

Additional Math Textbook Solutions

To find:

a. The centre $(h, k)$ and radius of the circle $x ² + y ² - x + 2 y + 1 = 0$

b. The graph of the circle

c. Intercepts of the circle, if any