In (x-h)^2+(y-k)^2=r^2 and if the center is (3,-5), does k becomes positive? or does it stay negative?

Yes, the equation has the center point subtracted from the variable.  In this case the coordinate is negative so it is like adding the coordinate to the variable because --=+

(y--5)^2=(y+5)^2

Ifound this on google “that means that the graph of a function with direct variation has these features: it is a straight line: because the slope is the ratio y/x = k. it passes through the origin (0,0): because y = kx = k (0) = 0.” i hope this you for what your looking for