 | Cambridge Philosophical Society - 1880 - 494 pages
...; it differs entirely from that given above, and depends on the simple property of a straight fine, viz. that it is the locus of a point which moves,...points,) whose lengths satisfy the single condition PE.EB = PF.FC, Fig. 2. BC being arbitrary. • Let the links be placed so that the angles at E and... | |
 | Arthur Le Sueur - 1886 - 120 pages
...the inclination of tho tangent is that of tho conjugate diameter. The Hyperbola. DEF. — A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points (the foci) is constant. The hyperbola may be treated in the... | |
 | Horatio Scott Carslaw - 1905 - 124 pages
...hyperbola whose equation is —^-'-jn—^Prove that SP = ex1-a, aud S'P=ex1 + a, and deduce that the curve is the locus of a point which moves so that the difference of its distances from two fixed points is constant. z2 if 5. The tangent at P on the hyperbola -2-p... | |
 | Charlotte Angas Scott - 1907 - 452 pages
...particular case that arises when the two foci come together. 4. Prove that the hyperbola ^ - -f- = 1 is the locus of a point which moves so that the difference of its distances from the two foci is equal to the major axis. 5. Prove that in Exs. 1-7, and in Ex.... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - 1917 - 384 pages
...its projection on a horizontal plane shall be a circle. Ans. 25° 50'. 161. Hyperbola. A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points is constant. The fixed points are called the foci. Other terms... | |
 | Maria M. Roberts, Julia Trueman Colpitts - 1918 - 266 pages
...transverse axis. This fact leads to a second and important definition of an hyperbola : An hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points is constant. м' From this definition, an hyperbola can be constructed... | |
 | Clyde Elton Love - 1927 - 288 pages
...hyperbola analogous to the one just proved for the ellipse leads to the following definition: A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points is constant. The fixed points are the foci and the constant... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale, John Haven Neelley - 1928 - 348 pages
...equal to its distance from a fixed line. Prove that the locus is a parabolic cylinder. 11. A point moves so that the difference between the squares of its distances from two intersecting perpendicular lines is constant. Prove that the locus is a hyperbolic cylinder. 13. A... | |
 | Stephen Barr - 1982 - 242 pages
...Anywhere on a hyperbola, with focus at F. The general definition of a hyperbola given in geometry books is: the locus of a point which moves so that the difference of its distances from two fixed points is constant. This is fulfilled by what is known to P of the... | |
 | 176 pages
...point which moves so that the sum of its distances from two fixed points is constant. The hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points is constant. We shall refer to this statement as the 'bifocal... | |
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The hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points, called foci, is a constant. This constant is equal to the length of the transverse axis. In Fig. 2-16, F and F' are the foci, and line AB,... 