A) p = 1 and q = 2 or 6
B) p = 2 and q = 0 or 6
C) p = 2 and q = 0 or 8
D) p = - 2 and q = - 2 or 8
Correct Answer: C
Solution :
Here equation is \[2{{x}^{2}}+4xy-p{{y}^{2}}+4x+qy+1=0\]. The lines are perpendicular, if \[a+b=0\] \[\Rightarrow 2-p=0\Rightarrow p=2\] and it will represent two lines, if \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\] \[\Rightarrow 2(-2)(1)+2\text{ }\left( \frac{q}{2} \right)\text{ }(2)\text{ }(2)-2{{\left( \frac{q}{2} \right)}^{2}}+2{{(2)}^{2}}-1{{(2)}^{2}}=0\] \[\Rightarrow {{q}^{2}}-8q=0\Rightarrow q=0\] or 8.
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