z varies directly with the sum of the squares of x and y

z = k (x^2 + y^2), where k is a constant

we will find k using the fact that z=10 when x =6 and y=2

10 = k(6^2 + 2^2)

k = 10/(6^2 + 2^2)

k = 10/40

k = 1/4

k = 0.25

the formula for z is

z = 0.25(x^2 + y^2).