Algebra II : Circle Functions
Study concepts, example questions & explanations for Algebra II
All Algebra II Resources
Example Questions
Example Question #481 : Functions And Graphs
Find the center and radius of the circle given the following equation:
The equation of a circle is in the format:
where 
Multiply two on both sides of the equation.
The equation becomes:
The center is 
The radius is 
The answer is:
Example Question #42 : Circle Functions
Determine the radius of the circle given by the following function:
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
When identifying the center of a circle, take the opposite sign of each value connected to x and y.
Example Question #91 : Quadratic Functions
What is the center and radius of the following equation, respectively?
The equation given represents a circle.
The center is at:
Set up an equation to solve the radius.
The radius is:
The answer is:
Example Question #22 : Center And Radius Of Circle Functions
Which of the following represents the formula of a circle with a radius of 
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:
Certified Tutor
All Algebra II Resources
