To find: the center and radius of each circle and graph the circle.
Answer to Problem 23RE
The center of the circle
Explanation of Solution
Given:
Calculation:
Group the terms containing x and the terms containing y . Bring the constant to theright side of the equation.
Express the terms within the parentheses as perfect squares. Any number added on the left-hand side must be added on the right-hand side also.
Factor the expression.
The standard equation of a circle with center
Express the equation in standard form
Compare the equation with the standard form.
Therefore, the center of the circle
The center of the circle is at the point (1, -2). Since the radius is 3 units, four points on the circle can be located by plotting points that are 3 units to the right, to the left, up, and down from the center. Use these points to graph the circle.
Substitute
Subtract 4 from both the sides.
Use the square root method.
Add 1 to both the sides.
The x -intercepts are
Substitute
Subtract 1 from both the sides.
Use the square root method.
Subtract 2 from both the sides.
The y intercepts are
Conclusion:
Therefore, the center of the circle
Chapter 1 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Calculus & Its Applications (14th Edition)
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