9.4. Ellipses http://www.ck12.org
9.4 Ellipses
Here you will translate ellipse equations from standard conic form to graphing form, graph ellipses and identify the
different axes. You will also identify eccentricity and solve word problems involving ellipses.
An ellipse is commonly known as an oval. Ellipses are just as common as parabolas in the real world with their own
uses. Rooms that have elliptical shaped ceilings are called whisper rooms because if you stand at one focus point
and whisper, someone standing at the other focus point will be able to hear you.
Ellipses look similar to circles, but there are a few key differences between these shapes. Ellipses have both an
x-radius and ay-radius while circles have only one radius. Another difference between circles and ellipses is that an
ellipse is defined as the collection of points that are a set distance from two focus points while circles are defined as
the collection of points that are a set distance from one center point. A third difference between ellipses and circles
is that not all ellipses are similar to each other while all circles are similar to each other. Some ellipses are narrow
and some are almost circular. How do you measure how strangely shaped an ellipse is?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61865http://www.youtube.com/watch?v=LVumLCx3fQo James Sousa: Conic Sections: The Ellipse part 1
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61867http://www.youtube.com/watch?v=oZB69DY0q9A James Sousa: Conic Sections: The Ellipse part 2
Guidance
An ellipse has two foci. For every point on the ellipse, the sum of the distances to each foci is constant. This is what
defines an ellipse. Another way of thinking about the definition of an ellipse is to allocate a set amount of string and
fix the two ends of the string so that there is some slack between them. Then use a pencil to pull the string taught
and trace the curve all the way around both fixed points. You will trace an ellipse and the fixed end points of the
string will be the foci. Foci is the plural form of focus. In the picture below, (h,k)is the center of the ellipse and
the other two marked points are the foci.