e preceding result is reconciled with that of §79, Cor. 1,by thinking of the polars (parallel) as turning about a point at in-finity. 15. The equation of the chord joining the points {x, y), {xf, y) on the ellipse is -/ ^ ^^ + ^^0, (§70, Eq. 2). Find the pole of this line ; and show that it lies on… … Let the direction-cosines of the parallel chords be Z, m, so that T m is that which passes through the The Ellipse. 161 centre; and let {a, (3) be the middle point of any oneof them: its equation is x-a_y-(3^I ~ m ~ whence x = a+ Jr, y = ^ + mr, Combinino- these with ~^ + ~ = l, we havea- ¥ ~ where…
Geometry, Analytic
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