Question

Find center and radius of circle 3x^2+3y^2+2x+6y+11=0

Answer 1

Step-by-step explanation:

Given equation of circle

$3 {x}^{2} + 3 {y}^{2} + 2x + 6y + 11 = 0$

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

Here,

$g = \frac{4}{3} \: and \: f = 1$

So,

$centre \equiv \bigg( - \frac{4}{3}, - 1\bigg)$

$radius = \sqrt{ \bigg( \frac{4}{3} \bigg)^{2} + (1)^{2} + \frac{11}{3} }$

$radius = \sqrt{ \frac{16}{9} + 1+ \frac{11}{3} }$

$radius = \sqrt{ \frac{16 + 9 + 33}{9} }$

$radius = \sqrt{ \frac{58}{9} }$