Given that the real number x.y satisfies (x-3) ^ 2 + (Y-3) ^ 2 = 6, find the maximum and minimum value of X + y It should be to find the tangent point of circle and line

Given that the real number x.y satisfies (x-3) ^ 2 + (Y-3) ^ 2 = 6, find the maximum and minimum value of X + y It should be to find the tangent point of circle and line

Let k = x + y, that is, the straight line x + Y-K = 0
When a line is tangent to a circle, the distance from the center of the circle to the line = radius
That is: | 3 + 3-K | / radical (1 + 1) = radical 6
|6-k | = root 12
6-k = root number 12
K = 6 root number 12
That is, the maximum value is 6 + 2 radical 3, and the minimum value is 6-2 radical 3

Given the real number x, y satisfies x + Y-3 ≥ 0, X-Y + 1 ≥ 0, X ≤ 2, if z = Y / x, find the maximum and minimum of Z

The feasible region is the gray part and the objective function is the green line
A(1,2),B(2,1)
 
So Zmax = 2
    zmin=1/2

Given that the real number x.y satisfies (X-2) ^ 2 + (Y-1) ^ 2 = 1, find the maximum and minimum of Z = y + 1 / X

1, z = (y + 1) / X.2, z = y + (1 / x)