A) \[(8,8)\] or \[(8,-8)\]
B) \[(4,8)\] or \[(4,-8)\]
C) \[(2,8)\] or \[(2,-8)\]
D) \[(16,8)\] or \[(16,-8)\]
Correct Answer: D
Solution :
Given, \[{{y}^{2}}=4x\] Let \[P(h,k)\] be any point on the parabola \[\therefore \] \[{{(h-1)}^{2}}+{{(k-0)}^{2}}={{17}^{2}}\] Alos, \[{{k}^{2}}=4h\] \[\therefore \] \[{{h}^{2}}+1-2h+4h=289\] \[\Rightarrow \] \[{{h}^{2}}+2h--288=0\] \[\Rightarrow \] \[(h+18)\,(h-16)=0\] \[\Rightarrow \] \[h=16\] ( \[\because \] h cannot be negative) \[\therefore \] \[{{k}^{2}}=64\] \[\Rightarrow \] \[k=\pm 8\] \[\therefore \] Points are \[(16,8)\] or \[(16,-8)\],
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