A family of lines is defined by (k−3)x+4y+5=0, where k is a real parameter.
a. (i) Find the value(s) of k for which this line is parallel to 2x−8y+7=0.
b. (ii) Find the value(s) of k for which the same line is perpendicular to 6x+3y−9=0.
c. (iii) State whether any value of k can satisfy both conditions obtained in parts (i) and (ii) simultaneously. Give a brief justification for your answer.