Forgot your password?  

Research Article: Family of Curves

This encyclopedia article consists of approximately 2 pages of information about Family of Curves.
This section contains 463 words
(approx. 2 pages at 300 words per page)
Purchase our Family of Curves Encyclopedia Article

Family of Curves

A family of curves is a collection of curves which share many of the same properties. For example, although there are infinitely many parabolas, all of them share the same basic shape. All parabolas consist of points which are equally distant from a fixed point, called the focus, and a fixed line, called the directrix. All have a vertex that is halfway between the focus and directrix. In fact, all parabolas can be seen as "descending" from a common "parent," the parabola whose algebraic representation is y=x2. This simplest of all parabolas has its vertex at the origin, its focus at the point (0,1/4) and its directrix with equation y=-1/4. Any other parabola can be "generated" from the y=x2 "parent" by one or more mathematical transformations. As an example, the parabola with equation (y-3)=(x-4) 2 can be created by translating the y...

(read more)

This section contains 463 words
(approx. 2 pages at 300 words per page)
Purchase our Family of Curves Encyclopedia Article
Follow Us on Facebook