sibNuaxiauoY

2022-11-26

Find the points on the cone ${z}^{2}={x}^{2}+{y}^{2}$ that are closest tothe point (2, 2,0).

Lauren Andrews

Expert

let the point be $d=\sqrt{\left(x-2{\right)}^{2}+\left(y-2{\right)}^{2}+{z}^{2}}$
Now for distance to be minimum
$2\left(x-2\right)+2x=0\phantom{\rule{0ex}{0ex}}⇒2x=2\phantom{\rule{0ex}{0ex}}x=1$

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