 | Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...ELLIPSE REFERRED TO THE Focus. The Focal Distances of any Point are SP=a- ex HP = a + ex 115 To find the Locus of a Point, the Sum of whose Distances from two fixed Points = 2rt 117 The Polar Equation (1) When the Focus is the Pole, is 1 + e cos 10 ' (2) When the Centre... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...Distances of any Point are SP — a — ex .*) HP — a + ex ............................... 115 To find the Locus of a Point, the Sum of whose Distances from two fixed Points = 2a ................ 117 The Polar Equation (1) When the Focus is the Pole, is 1 + e cos w ' (2) When... | |
 | John Hymers - Conic sections - 1837 - 486 pages
...method of investigating the equation to the ellipse which is sometimes employed as follows. 118. To find the locus of a point, the sum of whose distances from two given points is constant. Through the two fixed points S, H (fig. 40), draw the indefinite line Sx;... | |
 | Cambridge univ, exam. papers - 1847 - 40 pages
...extremities of any chord of a parabola intersect in the diameter which bisects the chord. fl. Find the locus of a point the sum of whose distances from two fixed points is constant. Shew how an ellipse whose semi-axes are 4 and 5 inches may be described mechanically. 14. Express the... | |
 | Isaac Newton, Percival Frost - Celestial mechanics - 1863 - 312 pages
...segments of a circle, which contain equal angles, are similar. 2. From the definition of an ellipse, as the locus of a point the sum of whose distances from two fixed points is constant, •shew that the ellipses are similar when the eccentricities are the same. 3. Prove that the center... | |
 | Charles Taylor - Conic sections - 1863 - 262 pages
...of two fixed planes. APPENDIX. In the following articles an Ellipse is considered to be defined as the 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... | |
 | Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...segments of a circle, which contain equal angles, are similar. 2. From the definition of an ellipse, as the locus of a point the sum of -whose distances from two fixed points is constant, 'shew that the ellipses are similar when the eccentricities are the same. 3. Prove that the center... | |
 | John Hunter (of Uxbridge.) - 1866 - 104 pages
...therefore the required coordinates are a;'=5^, y'=~fs Ex. (4). Investigate the equation to the curve that is the locus of a point, the sum of whose distances from two given points is constant. Let S, H be the two fixed points, and take C the middle point of SH as origin.... | |
 | John Hunter (of Uxbridge.) - 1866 - 44 pages
...SP=HA+AP + SB-BP; but AP=BP; .'. HP + SP=HA + SB, the sum of the given radii, and therefore constant. And the locus of a point, the sum of whose distances from two given points is constant, is an ellipse. (See the 4th of the worked Examples.) 12. If a;', y' were... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...segments (external or internal) whose product is equal to a given constant, fc*. (III. 56, 59.) 172. Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant It. 173. Find the locus of a point the difference... | |
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Find the locus of a point the sum of whose distances from two given parallel lines is equal to a given length. 
