- What is the mathematical definition of this conic section and how does that definition play a role in the properties of the conic section and how it is shaped or formed?
The
mathematical definition of an ellipse is the set of all points of the distances
from two fixed points is constant. Whenever you take a point in the ellipse the
distance will always add up to the focus points which are constant. The definition
affects how the graph will look like. The shape of the ellipse is formed
depending where the bigger number is located, if under x or y. If under y then
the graph will be skinny. In the other hand if the bigger number would be under
x then it would be fat. Depending on the x and y will determine the type of
shape the ellipse will have.
- How does the focus (or foci) affect the shape of the conic section? (If you choose ellipses, you should include information about eccentricity in your response; if you choose parabolas, "p" should be a big focus... haha, get it? "p" is the distance from vertex to focus and it should be a big focus. Ok, moving on...)
The focus is inside the ellipse. The distance from the focus
to any point in the ellipse will always be the same no matter where the
distance is. The eccentricity of an ellipse should be under 1 and it is found
by dividing c/a. Depending on the eccentricity will determine the shape of the
ellipse. For instance, the bigger the eccentricity like .983 then the thinner
and longer it seems to be compared to an eccentricity of .533 which may look
somewhat rounder but not a circle.
- How do the properties of this conic section apply in real life? (While using the exact examples I gave you may be acceptable, I will be looking for some research, creativity, and thought. There is a lot out there!)
The properties of ellipses are everywhere for example the
race track is shaped as an ellipse. The shape of the track that is shown in
most races and done in competitions is shaped as an ellipse. Also, hockey rings
have the shape of an ellipse. There are many things that are shaped like
ellipses that we don’t even notice like the bicycle chains and the orbits of
the planets.
citations:
- http://mathforum.org/sanders/geometry/GP18Ellipse.html
- https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRc_CVAgh6-BZmbqowwrzzp5u1V_DcBS1PJgnyz72XeMiAZtrlEWg
- http://cdn1.bigcommerce.com/server5200/eaffa/products/40/images/135/new_titiam_brac__89797.1342445689.1280.1280.jpg
