Smart, Edward Howard · London : Macmillian and Co. · leaf 202
o TY. TY = square of tangent from T to the auxiliary circle = CT^ - sq. of radius of aux. 0 (for the ellipse), but = sq. of radius of aux. O - CT^ (for the hyperbola) (for in the latter case the foci lie on opposite sides of any 174 PROJECTIVE GEOMETRY tangent, and it follows that T necessarily… … Fig. 916. It appears that an ellipse always has a real director circle;a hyperbola only when AC > BC. In the rectangular hyperbola AC = BC, and the directorcircle becomes a point-circle at the centre of the curve. In the parabola the circle has an infinite radius, and thusbecomes a straight…
Geometry, Projective
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