## anonymous one year ago 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.

1. anonymous

@Hero plz help

2. anonymous

3. anonymous

OMG THANK YOU SO MUCH I NEED SLEEP OMG

4. anonymous

lol ok :)

5. anonymous

(3,0) and (–3,0) are to be the focal points of the ellipse right?

6. anonymous

yeah

7. anonymous

x^2/25+y^2/16=1 is that the equation for the elliptical flower bed?

8. anonymous

for this you want $\frac{ x2 ^{} }{ a2 } + \frac{ y2 }{ b2 } = 1$ and you want $a^{2} - b^{2} = 3^{2}$ 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 $\frac{ x^{2} }{ 5^{2} } + \frac{ y^{2} }{ 4^{2} } = 1$ that will make your foci (−3,0) and (3,0)

9. anonymous

ok I got that part but what about the hyperbolic flowerbed

10. anonymous

can you try

11. anonymous

I can't make up the value of A

12. anonymous

like I know x^2/a^2-y^2/b^2=1 and a^2+b^2=3^2

13. anonymous

for the hyperbola it will look like x2/ a2−y2/b2=1 and you want a2+b2=33 simplest way i can think to do it is to make a2=8,b2=1 and use x2/8−y2=1 but you have other choices

14. anonymous

how did you get 33?

15. anonymous

no its $3^{3}$

16. anonymous

ok

17. anonymous

medal and fan please

18. anonymous

yeah but one more question how do you graph the second one?

19. anonymous

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

20. anonymous

ok thank you so much!!

21. anonymous

22. anonymous

medal and fan?

23. anonymous

yeah i already did

24. anonymous

ok thanks :)