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THE simplest property of the hyperbola is that it is the locus of a point the difference of whose distances from two fixed points is constant. The two fixed points are called tho foci.
Elements of analytic geometry - Página 163
de Simon Newcomb - 1885 - 356 páginas
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## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 páginas
...distances of any point in the curve from the foci is equal to the transverse axis. 165. Conversely, To find the locus of a point, the difference of whose distances from two fixed points S and II is constant or equal 2 a. If SH = 2 c, the locus is an hyperbola, whose axes are 2 a and 2...
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## An Analytical System of Conic Sections: Designed for the Use of Students

Henry Parr Hamilton - 1834 - 207 páginas
...HYPERBOLA REFERRED TO THE Focus. The Focal Distances of any Point, are SP=ex— a HP=ex + a 199 J^ To find the Locus of a Point, the difference of whose Distances from two fixed Points = 2a 201 The Polar Equation (1) When the Focus is the Pole, is - e'-l r = a — — , 1 + e cos w (2)...
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## An Analytical System of Conic Sections: Designed for the Use of Students

Henry Parr Hamilton - 1834 - 207 páginas
...equation to the hyperbola may be deduced, as in the analogous case of the ellipse, Art. 117201 . To find the locus of a point, the difference of whose distances from two Jixed points is always equal to a given quantity 2 a. Let S, H be the two fixed points, P the point...
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## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...the square on В С . . . • й 164. SP = e*-a,HP = ex+o, HP — SP = AA' . . • Sî 165. To find the locus of a point the difference of whose distances from two t¡»"< points is constant ........•• 166. The equation to the tangent is У j ~™ * * * 167....
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## A Treatise on Conic Sections and the Application of Algebra to Geometry

John Hymers - 1837 - 130 páginas
...property also furnishes the following method of investigating the equation to the hyperbola. 170. To find the locus of a point the difference of whose distances from two fixed points is constant. Through the two fixed points S, H (fig. 53) draw the indefinite line Hx, bisect SH in С and through...
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## Two Geometrical Memoirs on the General Properties of Cones of the Second ...

Michel Chasles - 1837 - 112 páginas
...property also furnishes the following method of investigating the equation to the hyperbola. 170. To find the locus of a point the difference of whose distances from two fixed points is constant. Through the two fixed points S, H (fig. 53) draw the indefinite line Hx, bisect SH in С and through...
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## An Analytical System of Conic Sections

Henry Parr Hamilton - 1843 - 276 páginas
...equation to the hyperbola may be deduced, as in the analogous case of the ellipse, Art. 152. 243. Tofind the locus of a point, the difference of whose distances from two foxed points is always equal to a given quantity 2 a. Let S, H be the two fixed points, P the point...
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## A collection of examples in pure and mixed mathematics, with hints and ...

1845
...nates for its centre ; trace this curve and find the magnitude of its axes. 1 73. Find the equation to the locus of a point the difference of whose distances from two fixed points is invariable ; and trace the curve. 174. The base of a triangle is constant, and the sum of the angles...
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## Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...Give a construction for drawing the equal conjugate diameters. 13. Defining an hyperbola to be th« locus of a point, the difference of whose distances from two fixed points is equal to a given line; shew what the general form of the hyperbola must be, and draw the conjugate...
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## Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - 1862 - 294 páginas
...2a1scy— sc*=o expressed by polar coordinates is ri=ai tan 20. Loci. Ex. 8. 1. Find the equation to the locus of a point the difference of whose distances from two fixed points is invariable ; and trace the curve. 2. The base of a triangle is constant, and the sum of the angles...
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