. Algebraic geometry; a new treatise on analytical conic sections . 218 PROPERTIES OF THE ELLIPSE. [chap. x. 240. If CP, CD are conjugate semi-diameters, SP. SP = 6 be the eccentric angle of P; then ^ + « i® *^® eccentricangle of D, and the co-ordinates of D are ( - a sin ^, J cos 6);.-. CD^ = a^sm^e + b^cos^e. SP = a-aecos6 and SP = a-t-fflecos^; (Art. 187).. = a2_a2«2cos2e = a2-(ft2_J2)cos2^ = a2sin2 5 + 62cos2 6» = CD2. 241. //CP, CD are conjugate semi-diameters, and tangents PT, DTare drawn at P and D, the area of the parallelogram PCDT = Let (a cos 9, I sin 6)


. Algebraic geometry; a new treatise on analytical conic sections . 218 PROPERTIES OF THE ELLIPSE. [chap. x. 240. If CP, CD are conjugate semi-diameters, SP. SP = 6 be the eccentric angle of P; then ^ + « i® *^® eccentricangle of D, and the co-ordinates of D are ( - a sin ^, J cos 6);.-. CD^ = a^sm^e + b^cos^e. SP = a-aecos6 and SP = a-t-fflecos^; (Art. 187).. = a2_a2«2cos2e = a2-(ft2_J2)cos2^ = a2sin2 5 + 62cos2 6» = CD2. 241. //CP, CD are conjugate semi-diameters, and tangents PT, DTare drawn at P and D, the area of the parallelogram PCDT = Let (a cos 9, I sin 6) be the co-ordinates of P,then (- a sin ^, h cos 6) are „ „ Fia. 143. Draw CK perpendicular to the tangent PT, whose equation is X cos 0 y sin 6 ^ , „ . , h^—T— = 1 or fa cos S H-ay sin 0 = ao. aCK = - ab / >^ + %i + C^ CD2 = a2sin2e-f-62cos2 0; .. CD = JWao^WVcM^d;the area of PCDT = CD . CK = a6 = AC . BC. ABT. 242.] PEOPEETIES OF THE ELLIPSE. 219 Corollary. The area of the parallelogram formed by tangents atthe ends of a pair of conjugate diameters = parallelogram = 4. PCDT = iab. 242. If the normal at P m^ets the major axis in G, and the diameterparallel to the tangent at P in F, PF. PG = BC^.Let (a cos 6, h sin 6) be the co-ordinates of P. As in Art. 225,


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