Using the following equation, find the center and radius: x2 + 2x + y2 + 4y = 20?

1 Answer
Jim G.
Jun 14, 2018

#"centre "=(-1,-2)," 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"#
#"the radius"#

#"to obtain this form "color(blue)"complete the square"#
#"on both the x and y terms"#

#x^2+2(1)x color(red)(+1)+y^2+2(2)y color(magenta)(+4)=20color(red)(+1)color(magenta)(+4#

#(x+1)^2+(y+2)^2=25larrcolor(blue)"in standard form"#

#"centre "=(-1,-2)," radius "=sqrt25=5#

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