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" Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line. "
A Text-book of Geometry - Page 403
by George Albert Wentworth - 1894 - 437 pages
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...whole line. 5. Given the base, area, and one of the angles at the base, construct the triangle. 6. Find the locus of a point which moves so that the sum of the squares of its distance from four given points is constant. On the Quadrature of a Rectilineal...
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Catalogue - Harvard University

Harvard University - 1873 - 732 pages
...given point parallel to a given plane ? parallel to a given line ? in. ANALYTIC GEOMETRY. 1. Determine the locus of a point which moves so that the sum of the Hquares of its distances from two fixed points is constant. Also determine the locus, changing...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - 1874 - 354 pages
...determine whether the straight line x + У = 2 +-/2 is a tangent or not. 17. Find the locus of a point, P, which moves so that the sum of its distances from two fixed points, A and B, is constant. 1870. July 19th. — Examiners, — Prof. HJS SMITH, MA, FRS, and Prof. SYLVESTER,...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...II. THE ELLIPSE. Definitions. 9. An ellipse is a plane curve that may be generated by a point, moving so that the sum of its distances from two fixed points is equal to a given line. The moving point is called the generatrix; the fixed points are foci ; the straight...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...fixed points. In what case does the conic degenerate into two intersecting straight lines ? 45. Find the locus of a point which moves so that the sum of the squares on the tangents drawn from it to the ellipse, -—- - + —jf = 1, is constant. X a v'...
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Mathematical Problems on the First and Second Divisions of the Schedule of ...

Joseph Wolstenholme - Mathematics - 1878 - 538 pages
...of the perpendiculars from any other point P, will bisect OP. [Such a polygon has the property that the locus of a point, which moves so that the sum of the squares on its distances from the sides is constant, is a circle.] 2254. The limiting position...
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London graduation mathematics, questions in arithmetic and algebra set from ...

Thomas Kimber - 1880 - 176 pages
...determine whether the straight line x + у = 2 +\/2 is a tangent or not, 17. Find the locus of a point, P, which moves so that the sum of its distances from two fixed points, A and B, is constant, 1870. July 19th. — Examiners, — Prof. HJS SMITH, MA, FRS, and Prof. SYLVESTER,...
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An elementary treatise on geometrical drawing

John Henry Robson - 1880 - 118 pages
...process as often as is required. Def.—An ellipse is the locus of a point which moves in such a way that the sum of its distances from two fixed points is constant. This accurate mathematical definition merely means that an ellipse is a curve traced out by the point...
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Conic Sections Treated Geometrically

S. Holker Haslam, Joseph Edwards - Conic sections - 1881 - 168 pages
...cut the curve will be the extremities of conjugate diameters. 105. If a point move in such a manner that the sum of its distances from two fixed points is constant, prove that its distance from any one bears a constant ratio to its distance from some fixed line. 106....
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Conic Sections Treated Geometrically

S. Holker Haslam, Joseph Edwards - Conic sections - 1881 - 168 pages
...cut the curve will be the extremities of conjugate diameters. 105. If a point move in such a manner that the sum of its distances from two fixed points is constant, prove that its distance from any one bears a constant ratio to its distance from some fixed line. 106....
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