A family with a coincident member
8 written marks
Consider \(l_k:(k-2)x+2y=8\) and \(m_k:x+(k-1)y=-4\).
Part a · 3 marks
Find k for which the lines are perpendicular, checking any exceptional case.
Part b · 3 marks
Find k for which the lines have the same direction, and distinguish coincidence from distinct parallelism.
Part c · 2 marks
Find the intersection when \(\displaystyle k=2\).
Complete-answer checking, worked solutions and indicative written criteria.
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