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Hyperbolic center (Posted on 2024-02-06) |
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A variable circle in the xy-plane is tangent to the x-axis and
meets the y-axis at the points P and Q. If the circle varies in such
a way that the length of the segment PQ is always 2, show that
the center A of the circle lies on a hyperbola, and find the equation of this
hyperbola.
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