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.