Find the radius of the circle x^2 + y^2 - 4x + 6y = 12.

Equation of circle is :-

( x - a )² + ( y - b )² = r²

x² + a² - 2ax + y² + b² - 2yb = r²   ----(1)

We are given that ,

x² + y² - 4x + 6y = 12   ----(2)

On comparing equation 1 and 2.

-2ax = -4x

a = 2

So, a² = 4

& -2yb = 6y

b = - 3

b² = 9

And a² + b² - r² = - 12

4 + 9 - r² = - 12

r² = 25

r = 5

So, Radius of circle = 5