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" Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k. "
Chauvenet's Treatise on Elementary Geometry - Page 128
by William Chauvenet, William Elwood Byerly - 1887 - 322 pages
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...rectangle AS, S A' = the square on В С 93 164. SP= ex—a,HP = ex+a, HP — SP = AA' .... 93 165. To find the locus of a point the difference of whose distances from two fixed points is constant ........ . 9J 166. The equation to the tangent is 167. The rectangle С T,...
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An Analytical System of Conic Sections: Designed for the Use of Students ...

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...
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An Analytical System of Conic Sections: Designed for the Use of Students

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 — — ,...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...A' = 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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Two Geometrical Memoirs on the General Properties of Cones of the Second ...

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,...
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A Treatise on Conic Sections: And the Application of Algebra to Geometry

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,...
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A collection of examples in pure and mixed mathematics, with hints and ...

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...
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

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...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863 - 482 pages
...ellipse. Give a construction for drawing the equal conjugate diameters. 13. Defining an hyperbola to be the 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...
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Geometrical Conics Including Anharmonic Ratio and Projection: With Numerous ...

Charles Taylor - Conic sections - 1863 - 262 pages
...locus of a point, the sum of whose distances from two fixed points is constant; and a Hyperbola as the locus of a point the difference of whose distances from two fixed points is constant. In either case it is easily seen that the constant length is equal to A A'...
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