SImple radius question?

Question

Is the radius of

x^2 - 6x + y^2 + 4y = 36

7? If it's wrong, can you tell me why? Thanks!

Answer 1

Equation of standard circle is:-
x² + y² + 2fx + 2gy + c = 0
Centre (- f , - g)
radius = √ [ f ² + g ² - c ]

Equation of given circle is:-
x ² + y ² - 6x + 4y - 36 = 0
2f = - 6
f = - 3

2g = 4
g = 2

c = - 36

r ² = g ² + f ² - c
r ² = 4 + 9 + 36
r ² = 49
r = 7

We appear to agree!

Answer 2

x^2 - 6x + y^2 + 4y = 36

completr the squares

x^2 - 6x + 9 + y^2 + 4y + 4 = 36 + 9 + 4

=>(x - 3)^2 + (y + 2)^2 = 49 = 7^2

so radius = 7