A) \[\frac{\sqrt{15}}{2}\]
B) \[\frac{\sqrt{19}}{2}\]
C) \[\sqrt{\frac{15}{2}}\]
D) \[\sqrt{\frac{19}{2}}\]
Correct Answer: A
Solution :
Let point at minimum distance from O is \[(h,{{h}^{2}}-4)\] \[\therefore \]\[O{{P}^{2}}={{h}^{2}}+{{({{h}^{2}}-4)}^{2}}\] \[\frac{d(O{{P}^{2}})}{dh}=2h+2({{h}^{2}}-4)2h=0\] \[\Rightarrow \]\[h=\pm \sqrt{\frac{7}{2}},0\] \[{{\left( \frac{{{d}^{2}}(O{{P}^{2}})}{d{{h}^{2}}} \right)}_{h=\pm \sqrt{\frac{7}{2}}}}>0\] \[O{{P}_{\min }}=\sqrt{\frac{7}{2}+{{\left( \frac{7}{2}-4 \right)}^{2}}}=\frac{\sqrt{15}}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
