The sum of the squares of the distances of a moving point from two fixed points `(a ,0)a n d(-a ,0)` is equal to a constant quantity `2c^2dot` Find the equation to its locus.

Explanation

Let P(h,k) be any position of the moving point and let A(a,0),B(−a,0) be the given points. Then,


`PA^2+PB^2=2c^2`


⇒`(h−a)^2+(k−0)^2+(h+a)^2+(k−0)^2=2c^2`


⇒`h^2−2ah+a^2+k^2+h^2+2ah+a^2+k^2=2c^2`


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