Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
The Circle  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Start by writing the given equation of a circle in standard form: r^2 = (xh)^2 + (yk)^2. In the equation, since r is being squared, the radius is the square root of the constant value. In other words, if r^2= 36, the radius is 6. To find the coordinate of the center, extract the h and k values. Since the quantity is (xh), that means that the value of just "h" will have the opposite sign. In other words, if the quantity is (x3), then h = 3. If the quantity is (x+5), then h = 5.
Finding the center and the radius from a given equation. So whenever we're given a equation for a circle, to find the information that's in there all we have to do is get it to a form we recognize. What I have here is similar to an equation for a circle, but I have these coefficients on my x and y² terms.
Our equation for circles can have those, so the first thing we have to do is get rid of those coefficients. In this case we just want to divide everything by 2 and our coefficients will be 1. So dividing through we end up with x minus 4 quantity squared plus y minus 1 quantity squared is equal to 72 over 2 or 36.
So now we just need to think back to our equation for a circle and extract the information. We're equal to 36 and that 36 is our radius squared which tells me that my, let's use a different color, radius is going to be equal to 6.
Our center is just extracted from the x minus and y minus terms and we're just dealing with x minus the x coordinate, so we're just dealing with x minus 4, that tells me my x coordinate is 4 and y minus the y coordinate tells me that I'm looking at 1 for my y coordinate of the center.
Another way you can look at is just think about what value needs to make this 0 and that will always be your coordinate for the center of the circle. So x is 4 to make this 0, y is 1 to make that 0, therefore 4,1 is our center.
So when finding the center and the radius of a equation, make sure it's in a form you recognize, make sure your coefficients are 1 and then just relate it to an equation for a circle x minus h² plus y minus k² is to r².
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (11)
Need help with a problem?
Watch expert teachers solve similar problems.

The Circle
Problem 1 14,260 viewsEquation for a circle centered at (1,2) with radius 5.

The Circle
Problem 2 11,362 viewsGive the center and radius of the circle defined by
2(x − 4)² + 2(y − 1)² = 72 
The Circle
Problem 3 10,826 viewsGive the center and radius of the circle defined by
x² + y² + 6y − 2x − 15 = 0 
The Circle
Problem 4 10,760 viewsFind the equation of a circle that has a diameter with endpoints at (3,1) and (5,5).

The Circle
Problem 5 2,517 views 
The Circle
Problem 6 2,354 views 
The Circle
Problem 7 2,254 views 
The Circle
Problem 8 2,206 views 
The Circle
Problem 9 2,234 views 
The Circle
Problem 10 2,266 views 
The Circle
Problem 11 2,201 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete