Q.

If lines 2x - 3y + 6 = 0 and kx + 2y + 12 =0 cut the co-ordinate axes in concyclic points then the value of k is

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answer is 3.

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Detailed Solution

Line 2x - 3y + 6 = 0 meets the axe s at A(-3, 0) and B(0,2).Line kx + 2y + 12 = 0 meets the axes at D(0,-6) and c(-12/k, 0).since the points A, B, c and D are concyclic, points A and, C cannot be at the same side of origin (see figure).Also, points A, B, C and D will be concyclic if|OA|×|OC|=|OB|×|OD|⇒3×|12/k|=2×6⇒|k|=3
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If lines 2x - 3y + 6 = 0 and kx + 2y + 12 =0 cut the co-ordinate axes in concyclic points then the value of k is