 | Peter Guthrie Tait - Dynamics - 1899 - 74 pages
...homogeneous shell bounded by similar, similarly situated, and concentric ellipsoids. Geometry shows that the locus of a point, the ratio of whose distances from two given points is constant, is a sphere surrounding one of these points. It is shown below that, if matter be distributed over this... | |
 | 1902 - 170 pages
...similar, the ratio of their areas is equal to the duplicate ratio of their homologous sides. 11. Shew that the locus of a point, the ratio of whose distances from two given points is equal to a given ratio, is a circle. II. 1 . Shew that the. circumference of a circle varies as its... | |
 | Education - 1920 - 928 pages
...within the triangle, is the required point, 0. To prove the construction it should be proved that: The locus of a point the ratio of whose distances from two given points is constant, is a circle. This can easily be proved by analytic geometry. Since AD bisects angle A, and since FD bisects angle... | |
 | Civil Service Commission of Canada - Civil service - 1910 - 240 pages
...quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle. 6. Find the locus of points from which the tangents drawn to two given circles are equal. '. * r PLANE... | |
 | Alexander Ziwet, Louis Allen Hopkins - Geometry, Analytic - 1913 - 396 pages
...times as far from the point (a, 6, c) as from the origin. — 7. Show that the locus of the points, the ratio of whose distances from two given points is constant, is a sphere except when the ratio is unity. 8. Find the positions of the following points relative to the... | |
 | Ernest Brown Skinner - Annuities - 1913 - 264 pages
...distances of the point P from two fixed lines, viz. BR and BY, is constant. From geometry we know that the locus of a point, the ratio of whose distances from two fixed lines is constant, is a straight line. Therefore the graph of the equation y = ax + b, or of... | |
 | Linnaeus Wayland Dowling - Geometry, Projective - 1917 - 242 pages
...KG ~BC AK _AB The ratio AK :KC is therefore constant so long as K is on the circle. In other words: The locus of a point, the ratio of whose distances from two fixed points is a given constant, is a circle. This circle is known as the circle of Apollonius. 32.... | |
 | University of Calcutta - 1917 - 844 pages
...triangle divides 12 the opposite side internally in the ratio of the sides containing the angle. Find the locus of a point, the ratio of whose distances from two 7 fixed points is constant. Or, Prove that the ratio of the areas of two similar triangles is equal... | |
 | Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...rectangle contained by them. 17 8. If two triangles be equiangular to one another, they are similar. 17 9. The locus of a point, the ratio of whose distances from two given points is constant, is a circle. 17 SOLID GEOMETRY. Marks. (Time, 3 hours.) 1. Name and describe all the regular solids. 8 2. Define... | |
 | Peter Guthrie Tait - History - 2018 - 462 pages
...whether the spheres intersect or not. It is, in fact, what is called their Radical Plane. 234. Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a. Also let P be the required point... | |
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PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*. 
