Smart, Edward Howard · London : Macmillian and Co. · leaf 180
A . , .,• • 6 = ;^ = ;^T7 in l>otn cases.CA CX dq2 RC^ .-. by § 2, c = 1 - ^ (ellipse) or 1 + ^ (hyperbola). e is therefore less than 1 in the former case and greaterthan 1 in the latter. For the parabola, since SA = AX, 6 = 1. From Fig. 76 we have then SP=PK, where P is any pointon the curve;… … Fig. 78a. Fig. 786. For Figs. 78a and h, SP pk _SP~PK^ e = SP + SP SPtSP smcebut PK ± PK KK PK + PK = KK in the ellipse,PK - PK = KK in the hyperbola. THE FOCI 153 But KK = XX = 2CX, and CA = cCX for both curves... SP + SP = 2CA for the elhpse,and SP - SP = 2CA for the hyperbola. Ex. 1. Given a…
Geometry, Projective
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