# How to find the center and radius of #x^2+y^2-6x-10y=-9#?

##### 2 Answers

The centre is

#### Explanation:

We know that the general form of a circle looks something like this:

where

Therefore, the centre is

#### Explanation:

#"the equation of a circle in standard form is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#

#"where "(a,b)" are the coordinates of the centre and r"#

#"the radius"#

#"obtain this form by "color(blue)"completing the square"#

#"on both x and y terms"#

#x^2-6x+y^2-10y=-9#

#x^2+2(-3)x color(red)(+9)+y^2+2(-5)ycolor(magenta)(+25)=-9color(red)(+9)color(magenta)(+25)#

#(x-3)^2+(y-5)^2=25larrcolor(blue)"in standard form"#

#"centre "=(3,5)" and "r=sqrt25=5#