How do you find the center and radius of the circle given $x^2+y^2+2x+4y=9$ ?

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Answer 1 · 2016-11-25T20:26:19

The center is $(-1,-2)$ and the radius is $sqrt14=3.74$

The equation of a circle, center, $(a,b)$ and radius $r$ is,

$(x-a)^2+(y-b)^2=r^2$

Let's complete the squares in the above equation

$x^2+2x+y^2+4y=9$

$x^2+2x+1+y^2+4y+4=9+1+4$

$(x+1)^2+(y+2)^2=(sqrt14)^2$

How do you find the center and radius of the circle given x^2+y^2+2x+4y=9x^2+y^2+2x+4y=9?