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To find: the center and radius of each circle and graph the circle.
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Answer to Problem 26RE
The center
Explanation of Solution
Given:
Calculation:
The standard form of an equation of a circle with radius r and canter
Simplify the given expression. For this, divide each term by 2.
In order to convert the given equation to standard form, complete the square in both x and y . Group the expressions involving x - and y -terms.
In order to complete the squares, take half the coefficient of x . Square the number and add it on both the sides of the equation.
Factor the equation.
The equation obtained can be rewritten as
On comparing the equation with the standard form, the values are obtained areh as 1, k as 0, and r as 1.
Thus, the center
In order to graph the circle, first plot the center
In order to find the x -intercepts, substitute 0 for y in the equation.
Take square root on both the sides.
Thus,
Solve for x ,
Thus, the x -intercepts are 2 and 0.
In order to find the y -intercepts, substitute 0 for x in the equation.
(0 - 1)2 + y2 = 1
1 + y2 = 1
Solve for y .
Subtract 1 from each side.
The y -intercept is 0.
Conclusion:
Therefore, the center
Chapter 1 Solutions
Precalculus
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