How do you find the center and radius of the circle given x^2+y^2+2x-10=0?

Mar 31, 2018

centre $C \left(- 1 , 0\right) \mathmr{and} r = \sqrt{11}$

Explanation:

The general equation of the circle:

${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0. \ldots \ldots \to \left(I\right)$,

whose centre $C \left(- g , - f\right) \mathmr{and}$ radius $r = \sqrt{{g}^{2} + {f}^{2} - c}$

We have,

${x}^{2} + {y}^{2} + 2 x - 10 = 0$

Comparing with $\left(I\right)$, we get

$2 g = 2 , 2 f = 0 , c = - 10$

i.e. $g = 1 , f = 0 , c = - 10$

So,

centre $C \left(- 1 , 0\right) \mathmr{and} r = \sqrt{{\left(1\right)}^{2} + {\left(0\right)}^{2} - \left(- 10\right)} = \sqrt{11}$