How do you find the center and radius of the circle x^2 + y^2 - 6x + 8y = 0?

1 Answer
May 26, 2018

"centre "=(3,-4)" and radius "=5

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"
"is the radius"

"use the method of "color(blue)"completing the square"
"on both the x and y terms"

x^2-6x+y^2+8y=0

x^2+2(-3)x color(red)(+9)+y^2+2(4)y color(magenta)(+16)=0color(red)(+9)color(magenta)(+16)

(x-3)^2+(y+4)^2=25larrcolor(blue)"in standard form"

"centre "=(3,-4)" and radius "=sqrt25=5