 | Charles Taylor - Conic sections - 1863 - 262 pages
...curve to the feet of the focal perpendiculars upon the tangent, will be the greatest possible. 66. Prove that the distance between the two points on...least angles, is equal to the diameter which bisects the chord. 67. In Ex. 61, prove that LP+ PL' is constant. 68. The rectangle contained by the radii... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...conjugate CD in V, prove that the areas of the triangles CA V, CPN are equal, PM being the ordinate. 44. Prove that the distance between the two points on...is equal to the diameter which bisects that chord. 45. A tansjent to an ellipse at a point P intersects a fixed tangent in T; if S is the focus and a... | |
 | William Henry Drew - Conic sections - 1869 - 153 pages
...in Q, and meets SP in R ; prove that PR is onefourth of the chord of curvature at P through 8. 47. Prove that the distance between the two points on...is equal to the diameter which bisects that chord. 48. From any point on the auxiliary circle chords are drawn through the foci of an ellipse, and straight... | |
 | William Henry Besant - Conic sections - 1875 - 348 pages
...join the ends of the axes. 44. Prove that the distance between the two points on the circumference, at which a given chord, not passing through the centre,...is equal to the diameter which bisects that chord. 45. The tangent at P intersects a fixed tangent in T; if S is the focus and a line be drawn through... | |
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Prove that the distance between the two points on the circumference of an ellipse, at which a given chord, not passing through the centre, subtends the greatest and least angles, is equal to the diameter which bisects that chord. 