A) \[\left( \frac{7}{2},1 \right)\]
B) \[\left( \frac{-1}{2},1 \right)\]
C) \[\left( -2,\frac{1}{2} \right)\]
D) \[\left( -\frac{7}{2},1 \right)\]
E) \[\left( -\frac{1}{2},-1 \right)\]
Correct Answer: D
Solution :
Given, \[{{y}^{2}}+6x-2y+13=0\] \[({{y}^{2}}-2y+1)=-6x-12\] \[{{(y-1)}^{2}}=-6(x+2)\] Let \[y=y-1\] and \[X=x+2\] then, \[{{Y}^{2}}=-6X\] ...(i) Which is equation of parabola whose vertex is\[(1,-2)\]and\[\left( a=\frac{3}{2} \right)\] Now, focus \[=(-a-2,1)\] \[=\left( \frac{-3}{2}-2,1 \right)\] \[=\left( -\frac{7}{2},1 \right)\]
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