Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 154
the origin. 123. Theorem III. The locus of the centres of parallelchords of an ellipse is a diameter. Proof. Let y = mx-{-h (a)be the equation of a chord; theslope m being the same for allthe chords, while h varies fromone chord to another. We first find the points of in-tersection of the chord… … which being reduced to the general form becomes _2aM_ a\h- b) _ + am -f Z^^^ ^ am + I Now we need not actually solve this equation to obtain THE ELLIPSE. 139 the result we want, namely, the abscissa of the middle pointof the chord. We know that if we put, for brevity, ^ ~ am + band call the roots…
Geometry, Analytic
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