xtodo math
- conic sections, can be defined by cutting a cone or quadratic equation.
- merge their definition.
- if cutting a cone, the plane must not pass thru the apex. if so, the degenerate conics is a point, line, or 2 intersecting lines.
- if by quadrtic equation, find the degenerate cases and describe them.
- define conics to be not degenerate
- convert all .nb notebook and delete them, to web page.
- define all conics to have consistent parameters, the distances a b c.
- center
- focus
- a is center to vertex.
- find 3d equation for right cone.
- find 3d equation for oblique cone.
- solve it with equation of plane, to find the equation of conics.
If the angle between the surface of the cone and its axis is β and the angle between the cutting plane and the axis is α , the eccentricity is cos α / cos β . [4]
- prove, that the cone is oblique or right cone no matter. show the parameters that change one to the other.
A parabola may also be defined in terms of its focus and latus rectum line (parallel to the directrix and passing through the focus): it is the locus of points whose distance to the focus plus or minus the distance to the line is equal to 2a; plus if the point is between the directrix and the latus rectum, minus otherwise.