My problem is from Israel Gelfand's Trigonometry textbook.
Page 9. Exercise 8: Two points, A and B, are given in the plane. Describe the set of points for which $AX^2-BX^2$ is constant.
I would appreciate some hints on how to approach the problem.
2026-05-17 03:28:28.1778988508
Points for which $AX^2-BX^2$ is constant
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We can use coordinate geometry, letting the two points be $(p,0)$ and $(-p,0)$, and grind it out. Not much grinding! If you prefer (I don't) you can let the points be $(a_1,a_2)$ and $(b_1,b_2)$.