SOLUTION: Please help.... In the example below give the centre and radius of the circle. {{{X^2+y^2-2x-6y+1=0}}} Thank you

Algebra ->  Circles -> SOLUTION: Please help.... In the example below give the centre and radius of the circle. {{{X^2+y^2-2x-6y+1=0}}} Thank you      Log On


   

Question 687969: Please help....
In the example below give the centre and radius of the circle.
X%5E2%2By%5E2-2x-6y%2B1=0
Thank you
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square for both x and y.

x%5E2%2By%5E2-2x-6y%2B1=0

x%5E2-2x%2By%5E2-6y%2B1=0

x%5E2-2x%2By%5E2-6y=-1

x%5E2-2x%2B1%2By%5E2-6y=-1%2B1

x%5E2-2x%2B1%2By%5E2-6y%2B9=-1%2B1%2B9

%28x-1%29%5E2%2B%28y-3%29%5E2=9

%28x-1%29%5E2%2B%28y-3%29%5E2=3%5E2

So the center is (1, 3) and the radius is 3.

Note: recall that the general form of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the length of the radius.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
In the example below give the centre and radius of the circle.
x^2+y^2-2x-6y+1=0
standard form of equation for a circle: (x-h)^2+(y-k)^2=r^2, (h,k)=(x,y) coordinates of center, r=radius
complete the squares:
x^2-2x+y^2-6y+1=0
(x^2-2x+1)+(y^2-6y+9)=-1+1+9
(x-1^2+(y-3)^2=9
center: (1,3)
radius:√9=3