Fan and Medal!! There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

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Fan and Medal!! There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

Mathematics
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for this you want x2a2+y2b2=1 and you want a2−b2=32 the easiest way to do that is to use the famous 3−4−5 right triangle and make a=5,b=4 so c=3 and use x252+y242=1 that will make your foci (−3,0) and (3,0)

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check the nice picture here to see that it works http://www.wolframalpha.com/input/?i=ellipse+x^2%2F25%2By^2%2F16%3D1
for the hyperbola it will look like x2a2−y2b2=1 and you want a2+b2=33 simplest way i can think to do it is to make a2=8,b2=1 and use x28−y2=1 but you have other choices
here is a nice graph with both together if you need one http://www.wolframalpha.com/input/?i=+x^2%2F8-y^2%3D1%2Cx^2%2F25%2By^2%2F16%3D1
reply if I helped
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