Thread: Center, Radius, and Standard Form

Hi all, I have a question I'm unsure of how to do. I might need a good explanation... I'm a little slow with math.

If (10,4) and (4,10) are the endpoints of a diameter of a circle, find the center of the circle, the radius of the circle, and the standard form of the circle's equation.

Originally Posted by Troy S

Hi all, I have a question I'm unsure of how to do. I might need a good explanation... I'm a little slow with math.

If (10,4) and (4,10) are the endpoints of a diameter of a circle, find the center of the circle, the radius of the circle, and the standard form of the circle's equation.

Hello, Troy.

Equation for a circle:

r^2 = (x - h)^2 + (y - k)^2, where the center is (h, k) and the radius is r.

You are given the ENDPOINTS of the diameter. Therefore, you should immediately think to use the MIDPOINT formula. That is, (h, k) = [(10 + 4)/2, (4 + 10)/2] = (7,7)

And now, use the equation above:

r^2 = (10 - 7)^2 + (4 - 7)^2 = 9 + 9 = 18

And therefore, we now have the equation:

(x - 7)^2 + (y - 7)^2 = 18 Standard form circle's equation that you are looking for

With this information, you should be able to answer all the questions regarding the circle (center of graph .. (h,k)), radius, etc, etc).

Great, thanks for the help.