Plane and solid analytic geometry; an elementary textbook . Draw MJST through Pl parallel to AB and continue theperpendicular OH to meet it at K. The equation of MNwill be x cos a + y sin a — p1 = 0, where px may be either positive or negative. For, as thevalue of a is fixed and as MN can be any line parallel toAB, it may be on the opposite side of the origin from AB,and in this case px will be negative. (See Art. 34.) Since Px lies on MN, its coordinates (xv y-^) must satisfythe equation of MN, 54 ANALYTIC GEOMETRY [Ch. IV, § 36 Hence xx cos a + yx sin a = pv Now wherever Px may lie, RPX = HK

---

Plane and solid analytic geometry; an elementary textbook . Draw MJST through Pl parallel to AB and continue theperpendicular OH to meet it at K. The equation of MNwill be x cos a + y sin a — p1 = 0, where px may be either positive or negative. For, as thevalue of a is fixed and as MN can be any line parallel toAB, it may be on the opposite side of the origin from AB,and in this case px will be negative. (See Art. 34.) Since Px lies on MN, its coordinates (xv y-^) must satisfythe equation of MN, 54 ANALYTIC GEOMETRY [Ch. IV, § 36 Hence xx cos a + yx sin a = pv Now wherever Px may lie, RPX = HK= OK- 011= px- p. Hence BPi = a?icosa + yisma-p, [17, a] If the equation is given in the form Ax + By +(7=0,it is necessary first to reduce it to the normal form andthen substitute xx for x and yx for y. Hence MP, = ±VJFTW • [IT, 8] TAe radical must be given the sign opposite to that of C. It appears from the way RPX has been chosen that theresult will be positive when the point and the origin are onopposite sides of the line ; negative, when they a

---

Size: 1381px × 1810px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No

Keywords: ., bookcentury1900, bookdecade1900, bookpublishernewyorkcscribnerss