# How do you find the radius of a circle with the equation #x^2 + y^2 + 4x - 8y + 13 = 0#?

##### 2 Answers

#### Explanation:

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

#"is the radius"#

#"to obtain this form "color(blue)"complete the square"" on both"#

#"the x and y terms"#

#x^2+4x+y^2-8y=-13#

#rArrx^2+2(2)xcolor(red)(+4)+y^2+2(-4)ycolor(magenta)(+16)=-13color(red)(+4)color(magenta)(+16)#

#rArr(x+2)^2+(y-4)^2=7larrcolor(blue)"in standard form"#

#rArrr^2=7rArrr=sqrt7#

#### Explanation:

Given: circle equation

The standard form of circle equation is:

where center

Use completing of the square to find the equation of the circle:

First combine the

To complete the square take

Add the extra added to the left side when you complete the square (

Simplify:

Since