what is the distance between the point A(3,8) and the circle (x^2+y^2+4x-6y) is equal to 12
The circle in standard form is
(x+2)^2 + (y-3)^2 = 25
So, consider the line through the center of the circle C=(-2,3) passing through (3,8).
That line will be perpendicular to the circle, so the distance from the circle will be the distance from C to A, less the radius of the circle r=5.
CA = √((3+2)² + (8-3)²) = √(25+25) = 5√2
So, the distance from A to the circle = 5√2 - 5 = 5(√2 - 1)