To find the constants 'a' and 'b', we first need to write the generic form of a quadratic function which has a minimum at some point 'r'. The general form of such a quadratic is f(x) = a(x-r)^2 + b.
Since we are given that the function has a local minimum at r = 1/5, our function becomes f(x) = a(x - 1/5)^2 + b.
Next, we substitute the condition f(1/5) = 1 into our equation. This gives us the equation 1 = a*(1/5 - 1/5)^2 + b. Simplifying this equation gives us b = 1.
Now, in order to find 'a', we need another point that lies on the curve. However, such a point has not been provided in this problem. Therefore, we won't be able to determine 'a' uniquely.
It's crucial to understand in this scenario that, given 'b', there are infinite possible parabolas (with different values of 'a') that go through the point (1/5, 1) and have a minimum at r = 1/5.
Therefore, without further information, we can't find a unique value for 'a'.
In conclusion, the constant 'b' is equal to 1 and 'a' can't be determined uniquely with the given conditions.