Algebra II : Circle Functions

Study concepts, example questions & explanations for Algebra II

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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:  

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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?  

Possible Answers:

Correct answer:

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 ?

Possible Answers:

Correct answer:

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:  

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