y^2+4x-20-2y=-x^2

Question

How to find the equation of this circle, the center of the circle and the radius.

Answer 1

The general form of the equation of a circle is 

Ax² +Ay² +Dx +Ey +F=0

In our case it is

y^2+4x-20-2y=-x^2 = x² + y² +4x -2y -20=0

so, we have the following expressions:

h=(-D/2A) = ((-4)/(2*1)) = 2 = x for the center

k=(-E/2A) = (2/2) = 1 = y for the center and for the radius is

r² =(D²+E² - 4AF)/4A² = 36

r= 6

Then the equation may be written:

(x-2)² + (y - 1)² =36