. Algebraic geometry; a new treatise on analytical conic sections . Fig. 139. Second method. Take the centre C, and join CP. , Draw any chord parallel to CP and bisect it at V. Join CV,and draw PT parallel to CV. PT is the tangent at P, for it isparallel to CV which is the diameter conjugate to CP. 216 PROPERTIES OF THE ELLIPSE. [chap. x. 237. To draw tangents to an ellipse from an external point T. T K -?==—°\ 2\\ /^ \y l^i\ ^ ^ ( t \L^?> v_ \ ^ X First method. Flo. 140. Draw TK perpendicular to the directrix, and with centre S (thecorresponding focus),and radius e. TK, de-scribe a circle.

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. Algebraic geometry; a new treatise on analytical conic sections . Fig. 139. Second method. Take the centre C, and join CP. , Draw any chord parallel to CP and bisect it at V. Join CV,and draw PT parallel to CV. PT is the tangent at P, for it isparallel to CV which is the diameter conjugate to CP. 216 PROPERTIES OF THE ELLIPSE. [chap. x. 237. To draw tangents to an ellipse from an external point T. T K -?==—°\ 2\\ /^ \y l^i\ ^ ^ ( t \L^?> v_ \ ^ X First method. Flo. 140. Draw TK perpendicular to the directrix, and with centre S (thecorresponding focus),and radius e. TK, de-scribe a circle. From T, draw tan-gents TR, TR to thiscircle. Join SR, SR andlet them meet theellipse at Q, Q respec-tively. TQ, TQ aretangents at Q and Qrespectively. The proof is similarto that in Art. 171. Second method. Draw the auxiliary Fio. 141. circle. On ST as diameter describe a circle cutting the auxiliary circle at Y and Z. Join TY, T2. TY, TZ are tangents to the ellipse.

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