3. 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.

Question

3.	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.

dontknowdontcare · Answer

I'm really stuck here, anyone help?

dontknowdontcare · Answer

@ganeshie8

dontknowdontcare · Answer

@hartnn @Mehek14

dontknowdontcare · Answer

@RhondaSommer

dontknowdontcare · Answer

@welshfella can you help?

welshfella · Answer

its been a while....

the equation of this ellipse  will be  

x^2 / a^2  + y^2 / b^2   =  1


the center will be at (0,0) and the value of a  will be  3   ( the distance from center to where  graph cuts y axis)

welshfella · Answer

so we have  

x^2          y^2
---   +     ---     =   1
 9              b^2

welshfella · Answer

sorry gtg right now 
I hope   someone else can help you

dontknowdontcare · Answer

@retirEEd can you help?

retireed · Answer

Sorry I was off researching how to do this and I am unfortunately still not sure how to do this question.

dontknowdontcare · Answer

Yeah, Im really stuck on it Thanks for trying though.

dontknowdontcare · Answer

@mrm sorry to bother but do you know this?

mrm · Answer

The a and b in your ellipse equation come from your points.  
So (-3,0) and (3,0) are equivalent to
$${(-\sqrt{a^2-b^2}, 0)\space and\space (\sqrt{a^2-b^2}, 0)}$$

mrm · Answer

This however is not enough information to create an ellipse.  The instructions require you to create two vertices on the y-axis.  The vertices should each be equal distance from the origin (0,0) so that the center of the ellipse is at (0,0).  So choose two points on the y-axis to create your vertices.  Do that now.

mrm · Answer

You can choose any two points you want.

mrm · Answer

Once you have your vertices (two points on the y axis) and you have you two foci (given)  You are equipped with all the information you need to find a and b fr you ellipse equation:
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
a is your major axis (the longest axis of the ellipse
b is your minor axis (the shortest axis of the ellipse)
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The equation for your hyperbola is 
$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$
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