How to find the coordinates of center of the circle with equation x^2 + y^2 – 20x – 16y + 139 = 0?

1 Answer
Jim G.
Apr 16, 2018

#"centre "=(10,8)#

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"#

#"to obtain this form use the method of"#

#color(blue)"completing the square ""on both x and y terms"#

#"collecting x and y terms together"#

#x^2-20x+y^2-16y=-139#

#"add "(1/2"coefficient of x and y terms")^2" to both sides"#

#x^2+2(-10)xcolor(red)(+100)+y^2+2(-8)ycolor(magenta)(+64)=-139color(red)(+100)color(magenta)(+64)#

#rArr(x-10)^2+(y-8)^2=25larrcolor(blue)"in standard form"#

#"with centre "=(10,8)" and radius "=5#

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