A) A circle
B) Two straight lines passing through origin
C) Two straight lines passing through the point (5, 6)
D) None of these
Correct Answer: C
Solution :
\[{{(x-5)}^{2}}+(x-5)(y-6)-2{{(y-6)}^{2}}=0\] Þ \[{{x}^{2}}+25-10x+xy+30-6x-5y-2{{y}^{2}}-72+24y=0\] \[\Rightarrow {{x}^{2}}+xy-2{{y}^{2}}-16x+19y-17=0\] Obviously, it is not a circle as \[a\ne b\]and xy is present. On checking for pair of straight lines, we get that the equation represents a pair of straight lines. Also for \[x=5,\ y=6,\]equation vanishes. Therefore it passes through (5, 6).
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