"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"
(x-1)^2+(y-2)^2=64" has centre "(1,2)" and "r=8
(x+3)^2+(y-4)^2=9" has centre "(-3,4),r=3
"what we have to do here is "color(blue)"compare ""the distance"
"( d) between the centres to the "color(blue)"sum/difference of radii"
• " if sum of radii">d" then circles overlap"
• " if sum of radii"< d" then no overlap"
• " if difference of radii">d" then 1 circle inside other"
"to calculate d 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)=(1,2)" and "(x_2,y_2)=(-3,4)
d=sqrt((-3-1)^2+(4-2)^2)=sqrt(16+4)=sqrt20~~4.47
"sum of radii "=8+3=11
"difference of radii "=8-3=5
"since diff. of radii">d" then 1 circle inside other"
graph{((x-1)^2+(y-2)^2-64)((x+3)^2+(y-4)^2-9)=0 [-40, 40, -20, 20]}
