The graph of x^2 +x +y^2 +y゠ 199/2 in the xy-plane is a circle. What is the length of the circle's radius?

Solution:

General Equation of a circle is (x-h)2 + (y-k)2 = r2

Here we would transform the given equation in this form of general equation,

x2 + x + y2 + y = 199/2

x2 + x + y2 + y + (1/4) + (1/4) = (199/2) + (1/4) + (1/4)

[x2 + x + (1/4)] + [y2 + y + (1/4)] = (199/2) + (1/2) 

(x + 1/2)2 + (y + 1/2)2 = 100

On comparing the with the General Equation,  r2 = 100, so r = 10 and  h = -(1/2) and k = -(1/2)

We have Circle of Radius = 10 and it's centre lies at point (-1/2 , -1/2 )