The sum of the squares of the distances of a moving point from 2 fixed points A(a, 0) and B(-a, 0) is equal to a constant 2 c^2 , then the equation of its locus is

Step-by-step solution

Let the point be P(x, y) . Then, aligned & B P= (x+a)^2+(y-0)^2 & and A P= (x-a)^2+(y-0)^2 aligned Given that, (B P)^2+(A P)^2=2 c^2 i.e. (x+a)^2+y^2+(x-a)^2+y^2=2 c^2 aligned & x^2+a^2+2 a x+2 y^2+x^2+a^2-2 a x=2 c^2 & 2 x^2+2 y^2+2 a^2=2 c^2 & or x^2+y^2=c^2-a^2 aligned Desired locus is x^2+y^2=c^2-a^2