. Algebraic geometry; a new treatise on analytical conic sections . Pig. 77. .. r = 2a cos (^ - a), as before. on the circle, 0 itscentre, and draw CKperpendicular to OP. ^0PC = ; = 6l-o; .. 0P=20K = 200 cos (5-a); .. r = 2aCOS(6-a)is the required equation. Alternative OB is the diameterthrough O, OP = OBcosPOB; 116 POLAR EQUATION OF A CIRCLE. [chap. 123. To find thepdUw equation of the tangent at the pmnt (rj, 6^) to the circle whose equa-tion is r = 2a cos (6-a). Let PK be the tan-gent at the pointP(rj, 6j), and draw OKperpendicular to it. If C(a, a) is thecentre of the
. Algebraic geometry; a new treatise on analytical conic sections . Pig. 77. .. r = 2a cos (^ - a), as before. on the circle, 0 itscentre, and draw CKperpendicular to OP. ^0PC = ; = 6l-o; .. 0P=20K = 200 cos (5-a); .. r = 2aCOS(6-a)is the required equation. Alternative OB is the diameterthrough O, OP = OBcosPOB; 116 POLAR EQUATION OF A CIRCLE. [chap. 123. To find thepdUw equation of the tangent at the pmnt (rj, 6^) to the circle whose equa-tion is r = 2a cos (6-a). Let PK be the tan-gent at the pointP(rj, 6j), and draw OKperpendicular to it. If C(a, a) is thecentre of the circle, aKPO = 2-^OP0 = h-aOOP =5-(^i-«); .-. OK = OP sin r^ - ((9j - a)1 = ri cos (6^ - a). Also L KOa; = LKOP + LPOx={ej^-a)+ 6^ = 26^-01 ■.. the equation of the tangent PK is 7-j cos(^j - a) = r cos{d - 26-^ + a), [p = r cos(6 - a)] 124. To find the polarequation of the circlewhose centre is at thepoint (c, 0) in the initialline and whose radiusis a. Q Let P(r, 6) be anypoint on the circle andC the centre of thecircle. From the A OPO, 0P2 + 002 _ 20P. 00 cos POC = CP2; [b^ + c^- 2bc cos A = ««].. r^ + c^- 2cr cos ^ = a^ is the equation required.
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