 | Pierce Morton - Geometry - 1830 - 584 pages
...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... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...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)... | |
 | Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...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... | |
 | Mathematics - 1835 - 684 pages
...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.... | |
 | John Hymers - Conic sections - 1837 - 486 pages
...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... | |
 | Michel Chasles - Cone - 1837 - 564 pages
...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... | |
 | Henry Parr Hamilton - Conic sections - 1843 - 318 pages
...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... | |
 | Alfred Wrigley - 1845 - 222 pages
...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... | |
 | Robert Potts - 1855 - 1050 pages
...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... | |
 | Alfred Wrigley - Mathematics - 1862 - 330 pages
...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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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. 
