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Establish a relation between $x$ and $y$ such that point $(x, y)$ is equidistant from points $(-2, 5)$ and $(3, 9)$.
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Solution: $$\begin{aligned}& (x + 2)^2 + (y - 5)^2 = (x - 3)^2 + (y - 9)^2 \\ & \Rightarrow x^2 + y^2 + 4x - 10y + 4 + 25 = x^2 + y^2 - 6x - 18y + 9 + 81 \\ & \Rightarrow 10x + 8y = 61\end{aligned}$$