 | Charles Smith - Conic sections - 1916 - 466 pages
...ePM, we have SP = eZN= e (ZC-+ CN) = e (- + x] = a + ex; \e I also An ellipse is sometimes defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. To find the equation of the curve from this definition.... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...across and 8 inches deep. How far is the focus from the vertex? Ans. 2 in. 157. Ellipse. An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points is constant. The fixed points F and F' (Fig. 110) are called the... | |
 | John Wesley Young, Frank Millett Morgan - Functions - 1917 - 586 pages
...method of its derivation is not applicable in this case. An ellipse could, therefore, be defined as the locus of a point which moves so that the sum of its distances from two fixed points (the foci) is constant. 226. Geometric Constructions of the Ellipse.... | |
 | Frederick Shenstone Woods - 1917 - 562 pages
...squares of its distances from the four sides of a square is constant. Find its locus. 123. A point moves so that the sum of the squares of its distances from any number of fixed points is constant. Find its locus. 124. Find the locus of a point the square of... | |
 | John Wesley Young, Frank Millett Morgan - Functions - 1917 - 584 pages
...P. 9. Find the equations of the common tangents of the circles z2+!/2=5 and x2 + y2 - 10 x + 20 = 0. 10. Find the locus of a point which moves so that the length of a tangent drawn from it to one given circle is k times the length of a tangent drawn from... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Calculus - 1917 - 536 pages
...center of the circle used in constructing it, the axes being parallel to those of § 47. 117. Show that the locus of a point which moves so that the sum of its distances from two fixed straight lines is constant is a straight line. 118. Find the equations... | |
 | Raymond Benedict McClenon - Functions - 1918 - 264 pages
...— 1. a2 a2 — c2 This result, being the equation of an ellipse, establishes the following THEOREM. -The locus of a point which moves so that the sum of its distances from two fixed points is a constant greater than the distance between the points is an... | |
 | Maria M. Roberts, Julia Trueman Colpitts - Geometry, Analytic - 1918 - 266 pages
...a = major axis. This fact leads to a second and important definition of an ellipse : An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points is constant. From this definition, an ellipse can be constructed... | |
 | George Alexander Gibson, Peter Pinkerton - Geometry, Analytic - 1919 - 510 pages
...points on the x-axis equidistant from, the origin 0, and ABC is an equilateral triangle. Show that a point which moves so that the sum of the squares of its distances from the sides of the triangle is :j(M2 describes a circle. Find the radius and the coordinates of the centre,... | |
 | Alexander H. McDougall - Geometry - 1919 - 232 pages
...former. 47. Show that the points (4, 2), (6, 2), (5, 2 + V3) are the vertices of an equilateral Л. 48. Find the locus of a point which moves so that the sum of its distances from the axes is 10. Trace the locus on squared paper. 49. Find the locus of a point... | |
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Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from... 
