Plane and Solid Analytic Geometry; An Elementary Textbook
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Plane and Solid Analytic Geometry; An Elementary Textbook

Plane and Solid Analytic Geometry; An Elementary Textbook


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 Excerpt: ...to the asymptote at the point where it is cut by the directrix. 8. Show that the product of the two perpendiculars let fall from any point of an hyperbola on the asymptotes is constant. 68. Conjugate hyperbolas.--If, in deriving the equation of the conic, the directrix is taken as the X-axis, and a perpendicular to it through the focus as the Praxis, its simplest form, in the case of the hyperbola, is 1. If the definitions of a and b are interchanged, using b to represent the semi-transverse axis (which is here the real intercept of the hyperbola on the. P-axis), the equation becomes,, ., ti=_1' where a and b have the same values, are closely related. The transverse and conjugate axes of the first are respectively the conjugate and transverse axes of the second. Two hyperbolas which are so related are called conjugate hyperbolas, either being conjugate to the other. But it is convenient to speak of the first as the primary and the second as the conjugate hyperbola. The polar equation of the conjugate hyperbola, -aW differs from that of the primary hyperbola only in the sign of the second member. It therefore gives real values for joonly for those values of 6 which gave imaginary values for p in the primary hyperbolas. The conjugate hyperbola has therefore the same asymptotes as the primary, but is situated on the opposite sides of those asymptotes. The value of c(=Va2 + 62) is the same for both the primary and conjugate hyperbolas, and the four foci therefore lie on a circle having its centre at the origin. But for the conjugate hyperbola e' =-, and the equations of the directrices are y = --., e' 69. Equilateral or rectangular hyperbola.--If b = a, the equation of the hyperbola becomes x2--y2 = a2. This is called the equilateral hyperbola. The equa...


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Product Details
  • ISBN-13: 9781231169230
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 48
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1231169230
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 104 gr

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