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

4 3 5 2

5

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