A) \[{{y}^{2}}-4x-2y+9=0\]
B) \[{{y}^{2}}+4x+2y-9=0\]
C) \[{{y}^{2}}-4x+2y+9=0\]
D) \[{{y}^{2}}+4x-2y+9=0\]
Correct Answer: C
Solution :
Since, focus is \[(3,\,\,-1)\] and vertex is\[(2,\,\,-1)\]. Here we see that \[y-\]coordinate is same, it means axis of the parabola is parallel to \[x-\]axis. Here, \[a=3-2=1\] \[\therefore \]Equation of parabola is \[{{(y+1)}^{2}}=4.1(x-2)\] \[{{y}^{2}}+2y+1-4x+8=0\] \[\Rightarrow \] \[{{y}^{2}}+2y-4x+9=0\]
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