 | George Salmon - Geometry, Analytic - 1862 - 490 pages
...one or other of the two kinds already discussed, according to the sign of the fraction — ^ — . In the case of the elliptic paraboloid therefore where...distance being measured parallel to a directive plane z = mx. Then a parallel plane through x'y'z', viz. z — z' = m(x — a;'), meets the directrix in... | |
 | Kansas Academy of Science - Science - 1890 - 206 pages
...to either imaginary directrix is — . £ The distance of any point on an ellipse from an imaginary focus is in a constant ratio to its distance from the corresponding directrix; this ratio is equal to the imaginary eccentricity of the conic. The equation of the tangent at the... | |
 | Charles Taylor - Mathematics - 1881 - 486 pages
...do. The projiosition will then take the form that " The distance of any point on a conic from cither focus is in a constant ratio to its distance from the corresponding directrix." either of its focal spheres, and MX the line in which it meets the plane of contact of the sphere with... | |
 | Kansas Academy of Science. Meeting - Science - 1890 - 222 pages
...center to either imaginary directrix is-. о The distance of any point on an ellipse from an imaginary focus is in a constant ratio to its distance from the corresponding directrix; this ratio is equal to .the imaginary eccentricity of the conic. The equation of the tangent at the... | |
| |
It is, that the distance of any point on the quadric from such a focus is in a constant ratio to its distance from the corresponding directrix, the latter distance being measured parallel to either of the planes of circular section. 