Locus Problem #3

Geometry Level 4

An ellipse with semi-major axis 2 2 and semi-minor axis 1 1 touches both the coordinate axis , then locus of its focus is :

( x 2 − y 2 ) ( 1 + x 2 y 2 ) = 16 x 2 y 2 (x^2-y^2)(1+x^2y^2)=16x^2y^2 ( x 2 + y 2 ) ( 1 − x 2 y 2 ) = 16 x 2 y 2 (x^2+y^2)(1-x^2y^2)=16x^2y^2 ( x 2 + y 2 ) ( 1 + x 2 y 2 ) = 16 x 2 y 2 (x^2+y^2)(1+x^2y^2)=16x^2y^2 ( x 2 − y 2 ) ( 1 − x 2 y 2 ) = 16 x 2 y 2 (x^2-y^2)(1-x^2y^2)=16x^2y^2

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