Question

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.

Answer 1

@Hero plz help

Answer 2

i can help you :)

Answer 3

OMG THANK YOU SO MUCH I NEED SLEEP OMG

Answer 4

lol ok :)

Answer 5

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

Answer 6

yeah

Answer 7

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

Answer 8

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)

Answer 9

ok I got that part but what about the hyperbolic flowerbed

Answer 10

can you try

Answer 11

I can't make up the value of A

Answer 12

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

Answer 13

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

Answer 14

how did you get 33?

Answer 15

no its \[3^{3}\]

Answer 16

ok

Answer 17

medal and fan please

Answer 18

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

Answer 19

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

Answer 20

ok thank you so much!!

Answer 21

your welcome

Answer 22

medal and fan?

Answer 23

yeah i already did

Answer 24

ok thanks :)