Answer:
Distance between \[(4,k)\] and \[(1,0)=5\] \[\sqrt{{{(1-4)}^{2}}+{{(0-k)}^{2}}}=5\] On squaring both sides \[9+{{k}^{2}}=25\] or \[{{k}^{2}}=25-9=16\] So \[k=\pm \,4\]
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