A) 3, - 3
B) - 3, 1
C) 3, 1
D) -1, 1
Correct Answer: A
Solution :
Given equation is\[{{x}^{2}}-{{y}^{2}}-x-\lambda y-2=0\]. Here, \[a=1\], \[b=-1\], \[c=-2\], \[h=0\], \[g=\frac{-1}{2}\], \[f=\frac{-\lambda }{2}\] This equation represents a pair of straight line, if \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\] \[2-\frac{{{\lambda }^{2}}}{4}+\frac{1}{4}=0\] Þ \[\frac{{{\lambda }^{2}}}{4}=\frac{9}{4}\Rightarrow {{\lambda }^{2}}=9,\,\lambda =\pm 3,\]i.e., (3, ? 3).
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