S_1, S_2 are two foci of the ellipse x^2+2y^2 = 2. P be any point on the ellipse The locus incentre of the triangle PSS_1

$$\displaystyle{S}_{{1}},{S}_{{2}}$$ are two foci of the ellipse $$\displaystyle{x}^{{2}}+{2}{y}^{{2}}={2}$$. P be any point on the ellipse The locus incentre of the triangle $$\displaystyle{P}{S}{S}_{{1}}$$, is a conic where length of its latus rectum is

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