2. To find the ellipse it has to be in standard conic form which is (x-h)^2/a^2+ (y-k)^2/b^2 = 1. It doesn't matter in what order a^2 and b^2 are they can be under whichever equation. h and k have to be in a specific one. H always has to be with x and k always has to be with y. another thing is that to determine the size of the ellipse if it's skinny or fat has to be based on x or y. If there ia a bigger number under x then it's fat, but if it's under the y then it's skinny. As you can see on the picture whatever d and d 2 are when they are added they equal 2a.
When graphed h,k will be center points. What ever numbers are on the bottom like we said then it place will be a and the second one b.vertices come from a, co-vertices from b, and foci from c and we find c from a^2-b^2=c^2. If a has bigger numbers then it's our major axis and b will be minor axis. The foci will be on the major axis but a little before the vertices points. To determine the eccentricity of an ellipse,is e = c/a. So it's whatever number is c comes out to be divided by whatever number a is. If it is still not clear the video on youtube below this will end up explaining how to solve the problem.
3.You can find ellipses in a training machine. "An elliptical training machine simulates the motion of running or climbing to provide the user with a healthful exercise without any impact on the joints." this helps the people to have better results little by little.
"The foot of a user describes the shape of an ellipse as the machine is used. An elliptical machine can be motor-driven or user-driven, as well as dual action, where handlebars and leg mounts interdependently provide motion for each other. The elliptical trainer provides a stationary exercise for those who wish to avoid joint injury as a result of running."
(http://www.ehow.com/info_8522010_real-life-uses-ellipses.html) this ellipse figure really helps the people that are trying to avid injuries so ellipses have a big impact on that.