The forewings are as in " Thioscelis directrix " except for the subterminal line, which is straighter, arising nearer the apex on the costa.
32.
In one solution of the former problem is the first recorded use of the property of a conic ( a hyperbola ) with reference to the focus and directrix.
33.
It is also possible to describe all conic sections in terms of a single focus and a single directrix, which is a given line not containing the focus.
34.
If the distance to the focus is fixed and the directrix is a line at infinity, so the eccentricity is zero, then the conic is a circle.
35.
The "'latus rectum "'is the chord parallel to the directrix and passing through the focus ( or one of the two foci ).
36.
Stodola established experimentally that the relationship between these three parameters represented in Cartesian coordinate system has the shape of a degenerate quadric surface, the cone directrix being an ellipse.
37.
The first to do so was apparently Pierce Morton in 1829 . The focus-directrix property is essential to proving that astronomical objects move along conic sections around the Sun.
38.
I doubt there is a intriguing focus-directrix type Locus definition for the curve of a y = x ^ 3 as there is for y = x ^ 2.
39.
As another example, a sideways parabola ( one whose directrix is a vertical line ) is not the graph of a function because some vertical lines will intersect the parabola twice.
40.
A proof that the conic sections given by the focus-directrix property are the same as those given by planes intersecting a cone is facilitated by the use of Dandelin spheres.
