To find the values of k, we apply the conditions for a line Ax + By + C = 0 based on the specific geometric properties requested. For part (a), a line is parallel to the x-axis only if the coefficient of x is zero (A=0). For part (b), a line is parallel to the y-axis only if the coefficient of y is zero (B=0). For part (c), similar to the concurrent lines example in the provided text where a point satisfies an equation, we substitute the origin's coordinates (0,0) into the given equation to find the required values.