You first need to learn how to complete the square or to factor.
For example,
1. x²+y²+4x-2y+1 = 0
Firstly, you need to arrange. Then, move the real whole number to the other side.
x²+4x+y²-2y = -1
Then, complete the square.
x²+4x+4 + y²-2y+1 = -1
We got 4 from the 4 in 4x in order to get the formula ax²+bx+c and we can find the c from b.
4÷2=2²= 4
Same with y²-2y+1.
2÷2=12=1
Now, when we added 4 and 1 from the left side, let's also add 4 and 1 to the right side.
x²+4x+4 + y²-2y+1 = -1+4+1
Lastly, let's factor to get the center and the radius.
x²+4x+4
Factor: (x+4)²
y²-2y+1
Factor: (y-1)²
x²+4x+4 + y²-2y+1 = -1+4+1
(x+4)²+(y-1)²=4
the center is (-4,1)
the radius is √4 or 2.
