Question

The circle C has centre A(2,1) and passes through the point B(10,7). Find and equation for C

Answer 1

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

$A(2,1) - \hbox{the centre} \\ h=2 \\ k=1 \\ \\ (x-2)^2+(y-1)^2=r^2 \\ \\ \hbox{passes through B(10,7)} \\ x=10 \\ y=7 \\ \\ (10-2)^2+(7-1)^2=r^2 \\ 8^2+6^2=r^2 \\ 64+36=r^2 \\ r^2=100 \\ \\ \hbox{the equation:} \\ \boxed{(x-2)^2+(y-1)^2=100}$