Can someone help me find the points on the surface "z^2 = x^2 + y^2" that are closest to the point (5,5,0)? - < #5.5.0 smtp;554 sorry, message looks like spam to me>

Surface points
(x, y, sqrt (x ^ 2 + y ^ 2))
and the distance from that point (5,5,0)
sqrt ((x-5) ^ 2 + (Y-5) ^ 2 + x ^ 2 + y ^ 2))
Now minimize this distance is the same as the place minizing
if we want to minimize
f (x, y) = (x-5) ^ 2 + (Y-5) ^ 2 + x ^ 2 + y ^ 2
This occurs when
df / dx = 0 and df / dy = 0 for
df / dx = 2 (x-5) x 2
df / dy = 2 (y-5) and 2
so that we
2 (x-5) 2 x = 0
4x = 5
x = 5 / 4
and
2 (y-5) 2 y = 0
4y = 5
y = 5 / 4

what is the point closest to (is 5,5,0)
(5 / 4 5 / 4, 5 * sqrt (2) / 4)