If the point P (x, y) is on the circle (X-2) ^ 2 + y ^ 2 = 3, then the sum of the maximum and minimum value of Y / X is? (seeking process.)

If the point P (x, y) is on the circle (X-2) ^ 2 + y ^ 2 = 3, then the sum of the maximum and minimum value of Y / X is? (seeking process.)

Let's use the parametric equation
X = √ 3cos θ + 2, y = sin θ, write the function y / x = sin θ / √ 3cos θ + 2, seek the derivative, take the extremum when cos θ = - √ 3 / 2, sin = + - 1 / 2,
The extremum of Y / X is 1, - 1 and the sum is zero
It should be OK to use linear programming,
If you draw a circle, Y / X is the slope of the line passing through the origin. Obviously, the slope is maximum and minimum when it is tangent, and it is symmetrical about the X axis, so the sum is 0