Find the equation of the locus of a point $P = (x, y)$ when the sum of the squares of the distances from $P$ to the points $(a, 0)$ and $(-a, 0)$ is $4b^2$, where $b \geq \dfrac{a}{\sqrt{2}}$?
2026-04-13 03:13:20.1776050000
Equation of the locus
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Well, you just "do the math"!
$y^2+(x-a)^2+y^2+(x+a)^2=4b^2$
is equivalent to
$y^2+x^2=2b^2-a^2$
The RHS is strictly positive, so...