A) \[-\frac{5}{3}\]
B) \[\frac{5}{3}\]
C) \[\frac{1}{3}\]
D) \[-\frac{1}{3}\]
Correct Answer: A
Solution :
Comparing the given equation with the standard equation, we get \[a=2,\ f=1,\ b=-k\], \[g=2,\] \[c=-1\] and \[h=2\]. Since equation represents a pair of lines, therefore \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\]or \[2\,k+8-2+4k+4=0\] or \[6k=-10\]. Therefore \[k=-\frac{5}{3}\].
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