# Algebra II : Circle Functions

## Example Questions

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### Example Question #19 : Center And Radius Of Circle Functions

Find the center and radius of the circle given the following equation:       Explanation:

The equation of a circle is in the format: where is the center and is the radius.

Multiply two on both sides of the equation. The equation becomes: The center is .

The radius is .

The answer is: ### Example Question #20 : Center And Radius Of Circle Functions

Determine the radius of the circle given by the following function:       Explanation:

To rewrite the given function as the equation of a circle in standard form, we must complete the square for x and y. This method requires us to use the following general form: To start, we can complete the square for the x terms. We must halve the coefficient of x, square it, and add it to the first two terms:  Now, we can rewrite this as a perfect square, but because we added 4, we must subtract 4 as to not change the original function: We do the same procedure for the y terms:   Rewriting our function, we get Moving the constants to the right side, we get the function of a circle in standard form: Comparing to we see that the radius of the circle is Notice that the radius is a distance and can therefore never be negative.

### Example Question #21 : Center And Radius Of Circle Functions      Explanation:

When identifying the center of a circle, take the opposite sign of each value connected to x and y.    ### Example Question #22 : Center And Radius Of Circle Functions

What is the center and radius of the following equation, respectively?       Explanation:

The equation given represents a circle.  represents the center, and is the radius. The center is at: Set up an equation to solve the radius. The radius is: The answer is: ### Example Question #23 : Center And Radius Of Circle Functions

Which of the following represents the formula of a circle with a radius of centered at ?      Explanation:

Write the standard form for a circle. The circle is centered at: The radius is: Substitute all the known values into the formula. Simplify this equation.

The answer is: 1 2 3 5 Next →

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