. Algebraic geometry; a new treatise on analytical conic sections . -a = ^;.. = ^TSP. 304. To find the equation of the chord of contact of- tcmgentsdram from the point (rj, 6j) to the conic -=l+e cos Let T be the point (r^, ^j),and TP, TQ, tangents to theconic. It is required tofind the equation of PQ. Tangents subtend equalangles at the focus,.. = ^TSQ = jB LTSX = e^,.. 6j - j8 is the angularCO ordinate of Q, and ^1 + ^ is the angularco-ordinate of P. .. the equation of PQmay be written :sec^cos(6i-^i)-l-«cose (1) (Art. 302.). I The equation of the tangent
. Algebraic geometry; a new treatise on analytical conic sections . -a = ^;.. = ^TSP. 304. To find the equation of the chord of contact of- tcmgentsdram from the point (rj, 6j) to the conic -=l+e cos Let T be the point (r^, ^j),and TP, TQ, tangents to theconic. It is required tofind the equation of PQ. Tangents subtend equalangles at the focus,.. = ^TSQ = jB LTSX = e^,.. 6j - j8 is the angularCO ordinate of Q, and ^1 + ^ is the angularco-ordinate of P. .. the equation of PQmay be written :sec^cos(6i-^i)-l-«cose (1) (Art. 302.). I The equation of the tangent TQ is - = cos{6 - 6^ + ^) + eeos6. ART. S05.] POLAR EQUATION OF A CONIC this line passes through the pofeit {r^, 6^);■■ — = cos ;8 + e cos flj. Whence sec/3 = ■ e cos 6, .. substituting this value of sec;8 in (1), the required equation is - = e cos 6 + y—i li, which may be written ecosO, {--eooBdjl—ecos6A = oos{6-0i). 305. Tangents to a conicat the ends of a focal chordintersect on the directrix. If PSQ is the focal chord,and a the vectorial angle ofP, the vectorial angle of Qis TT + a. .. the equations of the tangents TP and TQ are I r l_ r The second equation maybe written - = - cos(6 -a) + e cos 6. (2) - = COs(^-a) + 6COS0, (1); = cos(^ - JT - a) + ecos 6.
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Keywords: ., bookcentury1900, bookdecade1910, bookpublisherlondo, bookyear1916
