Explanation Given: Equation of the circle x ² + y ² − 6 x + 2 y + 9 = 0 Calculation:- x ² + y ² − 6 x + 2 y + 9 = 0 ( x ² − 6 x ) + ( y ² + 2 y ) + 9 = 0 ( x ² − 6 x ) + ( y ² + 2 y ) + 9 − 9 = 0 – 9 Subtract 9 from both sides ( x ² − 6 x + 9 ) + ( y ² + 2 y + 1 ) = − 9 + 10 Complete the square of each expression in parenthesis ( x − 3 ) ² + ( y + 1 ) ² = ( 1 ) 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 = 3 , k = − 1 and r = 1 . The circle has centre ( 3 , −1 ) and a radius 1 units. To graph the circle, first plot the centre ( 3 , −1 ) . Since the radius is 1 units, locate four points on the circle by plotting 1 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 ...

7th Edition

ISBN: 9780134119250

Author: Sullivan

Publisher: INTER PEAR

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Question

Chapter 1.5, Problem 30SB

To determine

To find:

1. The centre $(h, k)$ and radius of the circle $x ² + y ² - 6 x + 2 y + 9 = 0$

2. The graph of the circle

3. Intercepts of the circle, if any $- 23$

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Chapter 1.5, Problem 29SB

Chapter 1.5, Problem 31SB

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Chapter 1 Solutions

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Knowledge Booster

1. The centre ( h , k ) and radius of the circle x ² + y ² − 6 x + 2 y + 9 = 0 2. The graph of the circle 3. Intercepts of the circle, if any − 23

Solution Summary: The author explains how to find the circle's centre, radius, and x -intercepts.

To find:

1. The centre $(h, k)$ and radius of the circle $x ² + y ² - 6 x + 2 y + 9 = 0$

2. The graph of the circle

3. Intercepts of the circle, if any $- 23$

Want to see the full answer?

Chapter 1 Solutions

Additional Math Textbook Solutions

1. The centre ( h , k ) and radius of the circle x ² + y ² − 6 x + 2 y + 9 = 0 2. The graph of the circle 3. Intercepts of the circle, if any − 23

Solution Summary: The author explains how to find the circle's centre, radius, and x -intercepts.

To find: 1. The centre ( h, k ) and radius of the circle x² + y² − 6x + 2y + 9 = 0 2. The graph of the circle 3. Intercepts of the circle, if any −23

Want to see the full answer?

Chapter 1 Solutions

Additional Math Textbook Solutions

To find:

1. The centre $(h, k)$ and radius of the circle $x ² + y ² - 6 x + 2 y + 9 = 0$

2. The graph of the circle

3. Intercepts of the circle, if any $- 23$