ellipse help?

Question

what are the algebraic and geometric definitions of an ellipse?


also what is the importance of an ellipse in the world

Answer 1

An ellipse (why somebody else called it an eclipse, I have no idea) is the set of all points on a plane such that the sum of distances of each point to two fixed points is a constant. In other words, you set two points called the focus points, F1 and F2. Then P is a point on the ellipse if and only if the length of lines PF1 + PF2 = some constant.

Algebraically, the equation is in the form of
[ (x - h)^2 / a^2 ] + [ (y-k)^2 / b^2 ] = 1
where (h,k) is the center and "a" and "b" are constants such that the two axes are 2a and 2b.

As for where ellipses show up in the world, the orbits of planets travel around the sun in an ellipse. Comets also travel in an elliptical path. So astronomy is one place where you certainly find ellipses.

Answer 2

The geometric definition of an ellipse is:
The distance from one foci to another, through a point on the ellipse, is a constant.
The algebraic definition of an ellipse is:
(x - h)^2/a^2 - (y - k)^2/b^2 = 1

One feature of the ellipse or an ellipsoid of revolution is that light or sound emitted at one foci will all focus on the other foci.

All closed planetary and cometary orbits are ellipses with the major body at one foci and the minor body traveling along the ellipse. The orbits of the stars in their galaxies are ellipses.

Answer 3

An equation to show an eclipse is (x-h)/a^2+(y-k)/b^2=1
The importance of an eclipse? I didn't become a mathematician yet, nor have I been in the business world. Everything will become of use one day.