Question

find the center and radius of the circle 3x²+3y²-12x+6y+11=0​

Answer 1

$3x²+3y²-12x+6y+11=0$

$\sf \purple{dividing \: equation \: by \: 3}$

$\implies {x}^{2} + {y}^{2} - 4x + 2y + \frac{11}{3}$

$\implies {x}^{2} - 4x + {y}^{2} + 2y + \frac{11}{3} = 0$

$\sf \purple{making \: perfect \: square}$

$\implies {x}^{2} - 4x + 4 - 4 + {y}^{2} + 2y +1 - 1 + \frac{11}{3} = 0$

$\implies {(x - 2)}^{2} - 4 + {(y + 1)}^{2}- 1 + \frac{11}{3} = 0$

$\implies {(x - 2)}^{2} + {(y + 1)}^{2} \frac{11}{3} - 5 = 0$

$\implies {(x - 2)}^{2} + {(y + 1)}^{2}= 5 - \frac{11}{3}$

$\implies {(x - 2)}^{2} + {(y + 1)}^{2}= \frac{15 - 11}{3}$

$\implies {(x - 2)}^{2} + {(y + 1)}^{2}= \frac{4}{3}$

$\sf \purple{compring \: with \: standard \: equation}$

$\blue{ \boxed{ {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} }}$

$\orange{\therefore \sf centre = (2,-1)}$

$\orange{ \sf \color{white}{and } \orange{\: radius = \frac{2}{ \sqrt{3} } }}$

HOPE IT HELPS!

Answer 2

Answer:

radius=2/✓3 is the final answer