P(a,0) and Q(-a,0) are two fixed points. A point R, moves on the same side of PQ, so that `angleRPQ-angleRQP = 2alpha`, then
A. the locus of R is `x^(2) - y^(2) - 2xycot 2alpha - a^(2) = 0`
B. the locus of R is `x^(2) + y^(2) + 2xycot 2alpha - a^(2) = 0`
C. the locus of R is a hyperbola if `alpha = (pi)/(4)`
D. the locus of R is a circle if `alpha = (pi)/(4)`