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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antanasia220 · Answer

i dont remember how to do this im sorry

mww · Answer

This isn't too hard. Your focii are (-ae,0) and (ae,0). Now you can set up two equations for the hyperbola and the ellipse.

Recall for ellipse, $$b^2 = a^2(1-e^2) = a^2 - a^2e^2$$ 
and for hyperbola $$b^2=a^2(e^2-1) = a^2e^2 -a^2$$ 

Sub in $$a^2e^2$$ (being the square of ae) and you'll be able to write two equations with a and b and then find a and b.

likeabossssssss · Answer

welcome to os