How do you find the center and radius of the circle # x^2-2x+y^2-8y+1=0#?
You should convert to the form
Our goal here is to make the expressions in parentheses into perfect squares. We can use the formula
We need to add and subtract this number inside the parentheses to keep the equation equivalent.
The radius of a circle in the form
Hopefully this helps!
You complete the squares by adding
The standard Cartesian form for the equation of a circle is:
Equation  is the same as equation  but with the squares expanded and equation  is the given equation with some spaces added for missing terms:
Let's try to make equations  and  match by adding
Subtract 1 from both sides of equation  and label it equation :
Now that equation  and equation  both have 6 terms on the left side, we can see that we can find the value of h by equating the second term in equation  with the same term in equation :
Substitute 1 for h into equation  and number it equation :
We can find the value of k by equating the fifth term in equation  with the same term in equation :
Substitute 4 for k into equation  and number it equation :
Because we used the patterns for
Simplify the right side:
Comparing equation  with equation , we can see that the center is