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

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Jim G. Share
May 26, 2018

Answer:

#"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#

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