(adsbygoogle = window.adsbygoogle || []).push({}); how to find the "most far and most close" ( points on curve ) to another point ?

i'm studying a chapter on how to find maxima and minima values of a function using partial derivatives.

one of the problems is the following:

"if plane [itex]z=x+y+1[/itex] intersects cone [itex]z^2=x^2+y^2[/itex]

let the curve that result from intersection, is C

What is the most far and most close points on C, with respect to (0,0,0) ? and also with respect to [itex](x_1,y_1,z_1)[/itex]"

i think that that curve would be something like a circle, and that there would be some function that depends on the length between "(0,0,0) or [itex](x_1,y_1,z_1)[/itex]", and "any point on C".

But what is that function ?

And how to work out that problem ?

* i've exam in that chapter after about 10 hours, so please try to answer me with detailed answer as i've no time for discussions for now, may be i do that later.

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# How to find the most far and most close ( points on curve ) to another point ?

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