If one of the diameters of the circle, given by the equation x^2+y^2-4 x+6 y-12=0 , is a chord of a circle, 'S', whose centre is at (-3,2) , then the length of radius of ' S ' is ______ units.

Step-by-step solution

Find the radius of circle S given its center at (-3, 2) and that a diameter of C₁ is a chord of S . For circle C₁ defined by x^2+y^2-4x+6y-12=0 , comparing with the general form x^2+y^2+2gx+2fy+c=0 gives g = -2 , f = 3 , and c = -12 . The center of C₁ is (2, -3) and its radius is r₁ = g^2+f^2-c = 4+9+12 = 5 . The diameter of C₁ has length 10 and serves as a chord of S . The perpendicular distance from the center of S at (-3, 2) to this chord is the distance to the midpoint (2, -3) : d = (2+3)^2+(-3-2)^2 = 25+25 = 5