 | 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.... | |
 | 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.... | |
 | Charles Smith - Conic sections - 1883 - 452 pages
...equation - = 1 + e cos 6, shew that the ellipse might be generated by the motion of a point moving so that the sum of its distances from two fixed points is constant. 7. Find the locus of the pole of a chord which subtends a constant angle (2a) at a focus of a conic,... | |
 | Simon Newcomb - Geometry, Analytic - 1884 - 462 pages
...= a constant. 181. Cor. From §§ 97, 148 and 180 it follows that we may define a conic section as the locus of a point which moves in such a way that its distance from a fixed point (the focus) is in a constant ratio to its distance from a fixed straight... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...points and the focus, to find the directrix. THE ELLIPSE. 838. The locus of a point which moves so that the sum of its distances from two fixed points is constant is called an ellipse. The fixed points are called the foci, and the straight lines which join a point... | |
 | Evan William Small - Earth - 1894 - 296 pages
...planets are supposed to b° ellipses, instead of circles. (An ellipse is the curve which is traced out by a point which moves in such a way that the sum of its distances from two fixed points— -ff' Fig. 7 — remains constant. These two fixed points are termed l\\Q/oci of the ellipse, and the... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...major axis and is a line of symmetry. An ellipse may also be defined as the locus of a point moving so that the sum of its distances from two fixed points is constant. Exercises. — 1. Assume a point and a straight line and construct 7)r> o by points an ellipse having... | |
 | 1895 - 800 pages
...distances of any point on an ellipse is constant. Find the equation of the locus of a point which moves so that the sum of its distances from two fixed points is constant. 5. Find from the definition the differential coefficient of sin ./;, and deduce the differential coefficient... | |
 | Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...CHAPTER IX The Ellipse roo. The Ellipse. — An Ellipse is the locus of a point moving in a plane in such a way that the sum of its distances from two fixed points in the plane is constant. Let F and F' be the two fixed points in the plane. Let P be a point moving... | |
 | 1898 - 830 pages
...x = 0, > Show that its area is — 3. An ellipse is defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. Find from this definition the equation of the curve. 4. The equation of a circle is — x1 + у* -... | |
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PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. 
