A family of lines is defined by

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

(k-3)x + 4y + 5 = 0

, where

k

is a real parameter. (i) Find the value(s) of

k

for which this line is parallel to

2x - 8y + 7 = 0

. (ii) Find the value(s) of

k

for which the same line is perpendicular to

6x + 3y - 9 = 0

. (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.