A and B are foci of hyperbola 25(x−1)2+(y+1)2=k2(3x+4y+5)2,k>1 and P is a  variable point on hyperbola such that △APB is right angled isosceles triangle. If k=tan⁡α,α∈[0,2π] and sum of all values of α is aπ2b (where a and b are co-prime numbers), then