Smart, Edward Howard · London : Macmillian and Co. · leaf 195
asymptote is a tangent, the feet of the perpen-diculars from the foci on the asymptotes lie on the auxiliarycircle. It is easy to show that the directrices pass through the TANGENT AND NORMAL PROPERTIES 167 same points. For it has been proved that if X be the footof the directrix, CS. CX = CA^ (§… … Fig. 86. jlj 5. Prop. Tangents from an external point to a centralconic are eaually inclined to the focal distances of the point. Let SY, SY (Figs. 87a and b), SZ, SZ be the perpendicularsfrom the foci on the tangents from T. Then SY.SY = BC- = SZ .SZ (§3 (/>)). . SY _ SZSZ~STand angle YSZ =…
Geometry, Projective
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