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dontknowdontcare · Answer

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.

Maurice needs to plot two locations on a graph. He has to use the equation a2-b2=c2. We know that c=3, and a=6. We then plug that in to get, 62-b2=32. Multiply it out to get, 36-b2=9. b2=27 which you can then square root to find that b=5.196. Now we have to substitute what we know into the equation x2/a2 + y2/b2=1 and get x2/36 + y2/27=1. We know that c=3 so this time, I decided that a=1. You plug those in to get, 32=12+b2. Once you multiply out the exponents you should have, 9=1+b2. Subtracting 1 from both sides gives you, 8=b2. Square rooting both sides leads you to the conclusion that b=2.828. Next, to make the equation, we put in what we know to the equation. x2/a2 – y2/b2 = 1. x2/12 - y2/2.8282 = 1.

dontknowdontcare · Answer

I know I still have to make the graphs but

dontknowdontcare · Answer

@mathmate does this look good?

mathmate · Answer

Yes, with a=6, the ellipse is $x^2/36+y^2/27=1$
With a=1, the hyperbola is $x^2/1-y^2/8=1$, 
both have c=3
So your calculations are correct.
The vertices on the y axes can be solved for using the equations and setting x=0.

dontknowdontcare · Answer

So everything looks okay? @mathmate

mathmate · Answer

so far, yes.  You still have to finish the job finding two vertices on the y-axis.

mathmate · Answer

You will likely get help from more people by separating the steps into paragraphs.  Sometimes people are intimidated by a large paragraph full of words and numbers.  Mathematics tend to be simple and symbolic.
For example you could write the following to mean the same thing:
c=3 for both parabola and hyperbola
Parabola:
Set a=6
x^2/6^2+y^2/b^2=1  => b=sqrt(27)
vertices on y-axis: set x=0,
y^2/27=1  => y=....
Hyperbola:
Set a=1
x^2/1^2-y^2/b^2 = 1  => b=sqrt(8)=2sqrt(2)
vertices on hyperbola: set x=0,
y^2/8=1  => y=...