Solving Lagrange Problem Near (9,12,5)

[navalstudent]

Hi, I am supposed to find the point on the cone z^2=x^2+y^2 which is closest to the point(9,12,5).

here is my work:

http://img27.imageshack.us/my.php?image=lagrange001.jpg

Is it correct so far?

If it is: I get stuck when trying to solve the equations z^2=x^2+y^2, x=9/12*y, and -2xz+9z+5x=0. Can someone please give me some advice?

 

[Dick]

It looks to me like you are on the right track. Now use the second equation to eliminate x or y. It will work. Just keep going.