#"the equation of a circle in standard form is"#
#•color(white)(x)(x-a)^2+(y-b)^2=r^2#
#"where "(a,b)" are the coordinates of the centre and r"#
#"is the radius"#
#"here "(a,b)=(-4,-3)#
#" the radius is the distance from the centre to a point"#
#"on the circumference"#
#"to calculate r use the "color(blue)"distance formula"#
#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y_1)=(-4,-3)" and "(x_2,y_2)=(-3,3)#
#r=sqrt((-3+4)^2+(3+3)^2)=sqrt(1+36)=sqrt37#
#(x-(-4)^2+(y-(-3)^2=(sqrt37)^2#
#rArr(x+4)^2+(y+3)^2=37larrcolor(red)"equation of circle"#
#"the equation of a circle in "color(blue)"general form"# is.
#•color(white)(x)x^2+y^2+2gx+2fy+c=0#
#"to obtain this form expand the equation of the circle"#
#"and rearrange"#
#rArr(x+4)^2+(y+3)^2=37#
#rArrx^2+8x+16+y^2+6y+9-37=0#
#rArrx^2+y^2+8x+6y-12=0larrcolor(red)"general equation"#
