Sir please solve question number 2...................................

let P be (u, v).

now, write eqn of AP and BP. find the point of intersection of AP with line y= x (it will be an expression in a, u and v, for the time being lets call it (t, t)). similarly find the point of intersection of BP with line y= x (call it (z, z)).

then, k^2= (t – z)^2 + (t – z)^2

or k^2= 2(t – z)^2 

since t and z are already known in terms of a, u and v, we finally have an eqn in a, u, k and v. now simply replace u and v by x and y respectively, and as a and k are constant, we would finally have the reqd locus. the ques would be a bit lengthy, but ans aa jaega