A) \[7{{x}^{2}}+12xy-2{{y}^{2}}-2x+4y-7=0\]
B) \[11{{x}^{2}}+12xy+2{{y}^{2}}-10x-4y+1=0\]
C) \[11{{x}^{2}}+12xy+2{{y}^{2}}-14x-14y+1=0\]
D) None of these
Correct Answer: A
Solution :
\[S\,(1,\,1)\], directrix is \[2x+y=1\]and\[e=\sqrt{3}\]. Now let the various point be\[(h,k)\], then accordingly \[\frac{\sqrt{{{(h-1)}^{2}}+{{(k-1)}^{2}}}}{\frac{2h+k-1}{\sqrt{5}}}=\sqrt{3}\] Squaring both the sides, we get \[5[{{(h-1)}^{2}}+{{(k-1)}^{2}}]=3{{(2h+k-1)}^{2}}\] On simplification, the required locus is \[7{{x}^{2}}+12xy-2{{y}^{2}}-2x+4y-7=0\].
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