write the standard and general equation of the circle with center (-2,3), radius 5?

1 Answer
Jim G.
Jun 16, 2018

#"see explanation"#

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"#

#"here "(a,b)=(-2,3)" and "r=5#

#(x-(-2))^2+(y-3)^2=5^2#

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

#"the general equation of the circle is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(x^2+y^2+2gx+2fy+c=0)color(white)(2/2)|)))#

#"where centre "=(-g,-f)#

#"and radius "=sqrt(g^2+f^2-c)#

#"where "g^2+f^2-c>0#

#"to obtain the general form expand the standard form"#

#x^2+4x+4+y^2-6y+9-25=0#

#x^2+y^2+4x-6y-16=0larrcolor(red)"in general form"#

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