Conics

Given the base of a triangle and sum of its sides then the locus of the centre of its incircle is(A) straight line (B) circle(C) ellipse(D) hyperbola
Ans C

so p lies on ellipese.
now the question is to find the locus of incenter of triangle ps1s2.

@ashishdeosingh
How did you find h and k I didnt understand please explain

@nishantthakre
formulae for incenter