RWA: #1 Unit M Concepts 4-6

Ellipse

1. Mathmatical Definiton : "Set of all points such that the sum of the distance from two points is a constant." (Kirch)
2.  Algebraically defined: An ellipse can either be "fat" or "skinny". The eqaution for a fat graph is  (x-h)^2/a^2 +  (y-k)^2/b^2 =1, the bigger number "a" being on the bottom of x. If the graph is skinny then the eqaution of the graph is (x-h)^2/b^2 +  (y-k)^2/a^2 =1, the bigger number  "a" being below the y in this instance. In the eqaution, the If the bigger number is under the x thwn the graph is going to be fat and if the bigger number is under the y then the graph is going to be skinny. The center is (h,k). H always goes with x and K always goes with y.( Kirch) A skinny graph is going to have a vertical major axis, the axis which the foci lie on, therefore it will be x= #. A fat graph's major axis is going to have a horizontal major axis so it will be y=#. To find the veticies, co-vertices, and foci, you must first know what a,b, and c stand for. A be be derived from the standard eqaution. A being the biggest number and then the sqaure root being taken from it . B then being the second number . To find c , you must use the eqaution a^2-b^2=c^2 following the rule that a >b.(kirch) 

https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%253A%252F%252Fformula.algebra.com%252Fcgi-bin%252Fplot-formula.mpl%253Fexpression%253D%252528x-h%252529%25255E2%25252Fb%25255E2%252
B%252B%2B%2528y-k%2529%255E2%252Fa%255E2%2B%3D%2B1%26x%3D0003&container=
blogger&gadget=a&rewriteMime=image%2F 

http://formula.algebra.com/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+%2B+%28y-
k%29%5E2%2Fb%5E2+=+1&x=0003




Eccentricty is a measure  of how much the conic section deviates from being circular.(e=c/a) The ecccentricty of an ellipse must fall in the range of 0<e<1. To find the verticies, you must know the major axis. If the major axis is y=# then the term in the verticie that WILL NOT change will be the y term. However if the major axis is x=# then the term that will not change is the x term. To find the number that changes you must use the center . For example if the number is 5 and the term either a or b is 3 then you go up and down by 3 to get the number.  

The eccentricity of the graph determines how far away the ellipse deviates from being a circle. "An ellipse is defined in part by the location of the foci. However if you have an ellipse with known major and minor axis lengths, you can find the location of the foci using the formula below. The major and minor axis lengths are the width and height of the ellipse."(http://www.mathopenref.com/ellipsefoci.html) The foci will determine how far the ellipse deviates from being a circle since the eccentricty reqauires the use of "c",foci, divided by a.

3. REAL WORLD APPLICATIONS

https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%253A%252F%252Fupload.wikimedia.org%252Fwikipedia%252Fcommons%252
Fthumb%2F6%2F65%2FEllipse_Properties_of_Directrix_and_String_Construction.svg%2F411px-Ellipse_Properties_of_Directrix_and_String_Construction.svg.png&container=blogger&gadget=a&rewriteMime=image%2F*

The image displays how the distance from one point to another along the focus is the same all around ,such that it is a constant. It also displays the features of the graph and how it looks like. The foci on the major axis, the minor axis, and how to find the eccentricity.

  Math is indeed fun! The website explains ellipses and provides information about the conic section.
EXTREMELY AMAZING WEBSITE ------>http://www.mathsisfun.com/geometry/ellipse.html

  The video shows everything you would ever want to know about graphing ellipses and all the essential parts.
VIDEO HERE !!! ---------->http://www.youtube.com/watch?v=lvAYFUIEpFI

https://blogger.googleusercontent.com/img/proxy/AVvXsEh5h8peeuMDBHH8DVRZlR64Ik1UAuW61TCpu_yXnwzomn7rIPFgf-paPJe4B_k2CWt9YcFBn0wvP5hNLDrknjrGfuspZh889Ch3LzXBI8iQUT3p5tf_uPzSHUTSG2HZ1-JIHYP2UPzmLSBxpCsCx6-2rJU0hwNSIeRkdY98my0=
.png&container=blogger&gadget=a&rewriteMime=image%2F*

https://blogger.googleusercontent.com/img/proxy/AVvXsEhdFhpdGa65fdHHr0mTtDxzgNlURzeKWspsUScSARuOjWZ3o8RUHQX_paLd3-UZp0xKmhv64D66wVSV51oWdCDJ_XD6jjZdq-23xcgG74hdekqbSKDpq2rSm_ekHXZPi11bvlTUwLlDPzifO-0D8QRXWULYZSU=

This image basically just shows the features of the graph and how two lines from the focus are the same all around. It provides the eqaution to find the graph and "c". 

In the image it illustrates a real life example of a conic section. The distance around the conic from the foci is the same all around. In real life, the ellipse the most occuring "curve" seen beacuse the circle seen from an angle, is an ellipse(http://britton.disted.camosun.bc.ca/jbconics.htm) The reason why ellipses are the most common conic seen is because a circle veiwed a certain way is a ellipse. For example a tilted glass of water is an ellipse.Any cylinder sliced at an angle is also an ellipse. Each planet moves around the sun in an elliptical movement.

4. SITATIONS  http://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Ellipse_Properties_of_Directrix_and_String_Construction.svg/411px-Ellipse_Properties_of_Directrix_and_String_Construction.svg.png

http://www.physics.unlv.edu/~jeffery/astro/ellipse/ellipse_001.png

http://www.youtube.com/watch?v=lvAYFUIEpFI

http://www.mathsisfun.com/geometry/ellipse.html

http://britton.disted.camosun.bc.ca/elliplanet_lg.JPG

http://www.mathopenref.com/ellipsefoci.html

http://en.wikipedia.org/wiki/Eccentricity_(mathematics)

http://britton.disted.camosun.bc.ca/jbconics.htm

http://formula.algebra.com/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1&x=0003