Let x, y be real variable satisfying `x^(2) + y^(2) + 8x - 10y - 59 = 0` Let `a = max {(x-3)^(2) + (y-4)^(2)` and `b = min {(x-3)^(2) + (y-4)^(2))`, then a + b + 2010 is ______ .

Explanation

To solve the problem step-by-step, we start with the given equation of the circle:

### Step 1: Rewrite the Circle Equation
The equation given is:
\[ x^2 + y^2 + 8x - 10y - 59 = 0 \]

We can rewrite this in standard form by completing the square.

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