❤❤❤❤❤❤❤❤❤❤❤❤❤
[tex] {x}^{2} - 6x + {y}^{2} - y = 2[/tex]
Add sides 9 + 1 / 4
[tex] {x}^{2} - 6x + {y}^{2} - y + 9 + \frac{1}{4} = 2 + 9 + \frac{1}{4} \\ [/tex]
[tex] ({x}^{2} - 6x + 9) + ( {y}^{2} - y + \frac{1}{4} ) = 11 + \frac{1}{4} \\ [/tex]
[tex] ({x - 3})^{2} + ({y - \frac{1}{2} })^{2} = \frac{44}{4} + \frac{1}{4} \\ [/tex]
[tex] ({x - 3})^{2} + ( {y - \frac{1}{2} })^{2} = \frac{45}{4} \\ [/tex]
______________________________________
Remainder :
[tex] ({x - a})^{2} + ({y - b})^{2} = {R}^{2} [/tex]
[tex]center = ( \: a \: , \: b \: )[/tex]
[tex]radiuc = R[/tex]
______________________________________
Compare :
[tex] ({x - a})^{2} + ( {y - b})^{2} = {R}^{2} [/tex]
[tex]( {x - 3})^{2} + ({y - \frac{1}{2} })^{2} = ({ \frac{ \sqrt{45} }{2} })^{2} \\ [/tex]
Thus ;
[tex]center = ( \: 3 \: , \: \frac{1}{2} \: ) \\ [/tex]
[tex]radius = \frac{ \sqrt{45} }{2} = \frac{ \sqrt{9 \times 5} }{2} = \frac{3 \sqrt{5} }{2} \\ [/tex]
Done...
❤❤❤❤❤❤❤❤❤❤❤❤❤
