Plane and solid analytic geometry; an elementary textbook . semicubical parabola, and has the form shown in Fig. 98. 105 19G ANALYTIC GEOMETRY [Ch. XV, § 102 All parabolas are similar to one of these three formsaccording to the value given to n. Let the student plot the locusfor various values of n. Let himalso show that, if n is an eveninteger, or a fraction with an evennumerator and an odd denomina-tor, the curve is similar to theordinary parabola; if n is an oddinteger, or a fraction with an oddnumerator and an odd denomina-tor, the curve is similar to Fig. 97 ;while, if n is a fraction wit
Plane and solid analytic geometry; an elementary textbook . semicubical parabola, and has the form shown in Fig. 98. 105 19G ANALYTIC GEOMETRY [Ch. XV, § 102 All parabolas are similar to one of these three formsaccording to the value given to n. Let the student plot the locusfor various values of n. Let himalso show that, if n is an eveninteger, or a fraction with an evennumerator and an odd denomina-tor, the curve is similar to theordinary parabola; if n is an oddinteger, or a fraction with an oddnumerator and an odd denomina-tor, the curve is similar to Fig. 97 ;while, if n is a fraction with anodd numerator and an even de-nominator, the curve is similarto Fig. 98. 102. The Cassinian oval.—Thelocus of a point, the product ofwhose distances from two fixed points is constant, iscalled a Cassinian oval. The two fixed points are calledthe foci of the find its rectangularequation, let the X-axisgo through the two foci,F and F, and let theT-axis bisect FF. TakeOF equal to e, and let(x, y) be the coordi-nates of P, any pointon the Fig. 98.
Size: 1127px × 2217px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublishernewyorkcscribnerss
