Please help me if my answer is correct.
transform each equation into center radius form.
1. y2+x2-6y+5=0
y2+6y=(y+3)2=9
x2-5=(x-2)2=4
(y+3)2-9-(x-2)2=4
(y+3)2-9(x-2)2-4=+4
y^2+x^2-6y+5=0
If this is your starting equation
then:
x^2 + y^2 - 6y = -5
x^2 + y^2 - 6y + 9 = -5 + 9
x^2 + (y-3)^2 = 4
so centre of this circle is (0,3) and the radius is √4 or 2
the next two have "bouncing equal signs" , thus make no sense
the third one:
(y+3)^2-9-(x-2)^2=4
(y+3)^2 - (x-2)^2= 4 + 9
(x-2)^2 - (y+3)^2 = -13
this is a hyperbola with the foci on the y-axis
we don't use the term radius with hyperbolas.
I have no clue what the last one is, it sure looks like some typo variation
of the previous one.