A) \[(2\sqrt{2},0)\]
B) (0, 0)
C) \[(2,\,2)\]
D) None of these
Correct Answer: D
Solution :
Let a point on the curve by (h, k) Then \[{{h}^{2}}=2k\] ?..(i) Distance = D = \[\sqrt{{{h}^{2}}+{{(k-5)}^{2}}}\] By (i); \[D=\sqrt{2k+{{(k-5)}^{2}}}\] \[\frac{dD}{dk}=\frac{1}{2\sqrt{2k+{{(k-5)}^{2}}}}\times 2(k-5)+2=0\]\[x\in (-1,\infty )\] So, at \[k=4\] function D must be minimum. Then point will be \[(\pm \,2\sqrt{2},\,4)\].
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