Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author · New York, The Macmillan company · leaf 144
34] ELLIPSE AND HYPERBOLA 133 Just as in the case of the circle, so for the ellipse the locusof the midpoints of any system of parallel chords is a diameter.This follows from the corresponding property of the circlebecause the ellipse can be regarded as the projection of acircle (§121). But this… … Fig. 77 To find the diameter conjugate to a given diameter y = mxof the ellipse (1), let y=mx-\-k be any parallel to the givendiameter. If this parallel intersects the ellipse (1) at the realpoints (a!i, y^) and (aij, yi), the midpoint has the coordinates^(aji + ajj), 1^(2/1 + 2/2)- The quadratic…
Geometry, Analytic
Internet Archive · Cornell University Library · Public Domain Mark 1.0. Free to use for anything.
