Question

Can anyone explain to me how to graph a circle if it has a square root radius?
Example: x^2+y^2-7x=12-4y

The radius is √113/2, but I don't know how to graph it.

Answer 1

x^2 - 7 x = 12 - 4 y -y^2

x^2 -7x + 49/4 = 97/4 -4y -y^2

(x-7/2)^2 + y^2 + 4y =97/4

(x-7/2)^2 + y^2 + 4y + 4 =97/4+16/4

(x-7/2)^2 + (y+2)^2 = 113/4 sure enough

center at x=3.5 , y = -2
r = (1/2)sqrt(113) = 5.32

Answer 2

x^2+y^2-7x=12-4y
x^2 - 7x + 49/4 + y^2 + 4y + 4 = 12 + 49/4 + 4
(x - 7/2)^2 + (y+2)^2 = 113/4 = √113/2
you had that

so the centre is (7/2 , -2) and the radius is √113/2
which is appr 5.315

set you compass at appr 5.3 units, and with the above centre, draw your circle