Megan O’Donnell 3/27/13Reflection Entry #2 Pipitone Period 2

When I did the Ellipse Lab, I learned a lot about how to graph an ellipse both using a

calculator and not using a calculator. In order to graph a polar function you need; a graphing

calculator, a polar curve, pencils, an eraser, and an equation. I put the graphing calculator in

degree and polar modes after turning it on. I hit the “y=” button which in Polar mode is “r=” and

input the equation below.

In mathematics, an ellipse (from Greek ἔλλειψις elleipsis, a "falling short") is a plane curve that

results from the intersection of a cone by a plane in a way that produces a closed

curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the

cone's axis. An ellipse is also the locus of all points of the plane whose distances to two fixed

points add to the same constant. 

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is

constant leads to a method of drawing one using two drawing pins, a length of string, and a

pencil.[11] In this method, pins are pushed into the paper at two points which will become the

ellipse's foci. A string tied at each end to the two pins and the tip of a pen is used to pull the loop

taut so as to form a triangle. The tip of the pen will then trace an ellipse if it is moved while

keeping the string taut. Using two pegs and a rope, this procedure is traditionally used by

gardeners to outline an elliptical flower bed; thus it is called the gardener's ellipse.

The distance from the center C to either focus is f = ae, which can be expressed in terms of the

major and minor radii:

The eccentricity of the ellipse (commonly denoted as either e or  ) is

(where again a and b are one-half of the ellipse's major and minor axes respectively, and f is the

focal distance) or, as expressed in terms using

the flattening factor