Condition for a Conic to Be a Pair of Straight Lines
The value of ...
Question
The value of k for which the system of equations:
2x + 3y - 2z = 0; 2x - y + 3z = 0 and 7x + ky - z = 0 has non-trivial solution, is .
A
k=−575
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B
k=575
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C
k=−5710
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D
k=5710
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Solution
The correct option is Dk=5710 The given system of equations will have non-trivial solution if: D=⎛⎜⎝23−22−137k−1∣∣
∣∣=0⇒2(1−3k)−3(−2−21)−2(2k+7)=0⇒2−6k+69−4k−14=0⇒10k=57⇒k=5710