A) \[{{(x-1)}^{2}}=8(y-1)\]
B) \[{{(y-1)}^{2}}=8(x-3)\]
C) \[{{(y-1)}^{2}}=8(x-1)\]
D) \[{{(x-3)}^{2}}=8(y-1)\]
Correct Answer: C
Solution :
Given, vertex of parabola (h, k) \[\equiv \] (1, 1) and its focus \[(a+h,\,k)\equiv \,(3,\,1)\] or \[a+h=3\] or \[a=2.\] We know that as the y-coordinates of vertex and focus are same, therefore axis of parabola is parallel to x-axis. Thus equation of the parabola is \[{{(y-\,k)}^{2}}=4a\,(x-h)\] or \[{{(y-1)}^{2}}\] \[=4\times 2(x-1)\] or \[{{(y-1)}^{2}}=8(x-1).\]
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