Parabola拋物線的問題20分重酬

ok,i am sorry that i couldn't give you any picture,but i can still give you the information!
let's see what is it?
here:
In mathematics, the parabola (pronounced /pəˈræbələ/, from the Greek παραβολή) is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Given a point (the focus) and a line (the directrix) that lie in a plane, the locus of points in that plane that are equidistant to them is a parabola.

A particular case arises when the plane is tangent to the conical surface of a circle. In this case, the intersection is a degenerate parabola consisting of a straight line.

The parabola is an important concept in abstract mathematics, but it is also seen with considerable frequency in the physical world, and there are many practical applications for the construct in engineering, physics, and other domains.

In polar coordinates, a parabola with the focus at the origin and the directrix parallel to the y-axis, is given by the equation
r(1+cosx)=l


where l is the semilatus rectum: the distance from the focus to the parabola itself, measured along a line perpendicular to the axis. Note that this is twice the distance from the focus to the apex of the parabola or the perpendicular distance from the focus to the latus rectum.

The latus rectum is the chord that passes through the focus and is perpendicular to the axis. It has a length of 4l


Given a parabola whose axis of symmetry is parallel to the y-axis with vertex (0,0) and with equation
y=ax2

2008-10-30 16:50:07 補充：
i can give you more later,wait for me!

2008-10-30 16:50:32 補充：
A parabola may also be characterized as a conic section with an eccentricity of 1. A parabola can also be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction.

2008-10-30 16:50:50 補充：
parabola has a single axis of reflective symmetry, The point of intersection of this axis and the parabola is called the vertex. A parabola spun about this axis in three dimensions traces out a shape known as a paraboloid of revolution

2008-10-30 16:51:03 補充：
(with vertex (h, k) and distance p between vertex and focus - note that if the vertex is below the focus, or equivalently above the directrix, p is positive, otherwise p is negative; similarly with horizontal axis of symmetry p is positive if vertex is to the left of the focus,

2008-10-30 16:52:11 補充：
i am sorry that i couldn't give you the equations,because i can't "write" it down on YAHOO!
i am deeply sorry about it
hope these can help you!88^^