. Algebraic geometry; a new treatise on analytical conic sections . Fio. 121. 1+ The equation of RQ, the tangent at Q, is xh„ + J2 - ^- ART. 805.] POLE AND POLAR. But the point R (a;,, y-^ is on both these lines, and _0 t M ~ •j • 191 ■■(1)..(2) .-. y + M ^ 1^ or S + ^1 = 1 is the equation reqd. For firstly, it represents a straight from (1) we see that (a(A], h^ lies on this line,and „ (2) „ Q:{h^,h^ „ .. it is the equation of QQ, the chord of contact. 205. To find the polar of the point (aii, y-^ mth respect to the ellipse. Pro. 122. Let P be the point (a;,, y^) and DPE any cho
. Algebraic geometry; a new treatise on analytical conic sections . Fio. 121. 1+ The equation of RQ, the tangent at Q, is xh„ + J2 - ^- ART. 805.] POLE AND POLAR. But the point R (a;,, y-^ is on both these lines, and _0 t M ~ •j • 191 ■■(1)..(2) .-. y + M ^ 1^ or S + ^1 = 1 is the equation reqd. For firstly, it represents a straight from (1) we see that (a(A], h^ lies on this line,and „ (2) „ Q:{h^,h^ „ .. it is the equation of QQ, the chord of contact. 205. To find the polar of the point (aii, y-^ mth respect to the ellipse. Pro. 122. Let P be the point (a;,, y^) and DPE any chord through P; DQ,EQ the tangents at D and E. 192 THE ELLIPSE. [chap. X. It is required to find the locus of {Ji, h) be the co-ordinates of the equation of its chord of contact DE isxh yk _. But {x^, y^) is on this line, Also (h, h) is any point on the locus,.. the equation of the locus is x.,x y,y ,-\+^ = l, or a straight line. yyi 1, y ^^^^^V^J 1? ^ V. c J^ Q Fig. 123. When (aij, y{) is outside the ellipse, the polar is the same as thechord of contact of tangents drawn from {x^, y^). If the polar of the point P passes through the point Q, the polar ofthe paint Q, passes through the point P. This may be proved as in Art. 144. ART. SOT.] POLE AND POLAR. 193 206. Find the co-ordinates of the pole of the straight line lx + my + n = 0 vnth respect to the ellipse -3 + Ti= ¥ If (ajj, ^j) are the co-ordinates of the pole, the equations —^ + ^ = 1 and lx + my= -n are identical, for they represent the same straight
Size: 1741px × 1435px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookpublisherlondo, bookyear1916
