"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"
