GIVEN:
[tex]9x {}^{2} + 9y {}^{2} - 6x + 18y + 1 = 0[/tex]
SOLUTION:
CIRCLE EQUATION:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
REWRITE:
[tex]9x {}^{2} + 9y {}^{2} - 6x + 18y + 1 = 0[/tex]
IN THE FORM OF THE STANDARD CIRCLE EQUATION
[tex]( x - \frac{1}{3} ) {}^{2} + (y - ( - 1)) {}^{2} = 1 {}^{2} [/tex]
THERE FOR THE CIRCLE PROPERTIES ARE
(a,b)
[tex](a,b)=( \frac{1}{3} , - 1),r = 1[/tex]
FINAL ANSWER:
[tex] \large\orange{\boxed{Circle with center at (\frac{1}{3} , - 1)}}[/tex]
[tex]\large\green{\boxed{radius}{r=1}}[/tex]
