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Elements of analytic geometry (1884)

Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 206

An illustration from Elements of analytic geometry, 1884, leaf 206
i-diameter on which the point is taken divided by thedistance of the point from the centre. Polar of the Focus. Substituting {±ae, 0) for {x/ y) inthe equation of the polar, we have X = ±-.e Hence the polar of the focus of ayi hyperlola is the perpe^i- dicular which cuts the transverse axis at a… … FP FP therefore y^p = e. Whence: Theorem XI. The focal distance of any point on an hyper-bola is in a coristant ratio to its distance from the polar of thefocus. THE nYPERBOLA. 191 This ratio is greater than unity and equal to the eccentri-city of the curve. Def. The polar of the focus is called…

Geometry, Analytic

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