The standard equation for a circle is: (x-h)^2/a^2+(y-k)^2/a^2=1, where (h,k) is the centre and a is the radius. Substituting (-1,3) we have (x+1)^2/a^2+(y-3)^2/a^2=1. We also know that the circle passes through the point (2,4), so putting on these for (x,y) we get 9/a^2+1/a^2=1, so a^2=10. Therefore the equation of the circle is (x+1)^2+(y-3)^2=10.