Question

Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36.

Answer 1

@salehhamadeh

Answer 2

Can you get it to look like this:
\[\Large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]

Answer 3

these are the answer choices btw.

Answer 4

You need to change it to the form that @terenzreignz just mentioned. To do that, you divide both sides by 36 and then complete the squares of both the x and y. The form you get will be:
\[(x-x_0)^2/a + (y-y_0)^2/b = 1\]

Answer 5

ok let me try it!

Answer 6

The center will be (x0, y0)

Answer 7

I don't remember how to find the vertices and foci, but you can find the formulas easily in any algebra 2 or precalculus book. Once you get it into the form I mentioned above, all you need to do is plug the numbers into the formulas.

Answer 8

ok I'm having a bit of trouble getting it into that form

Answer 9

Where are you getting stuck?

Answer 10

1x^2/9+1y^2/4=1?

Answer 11

That's good. You can do away with those 1's...
\[\Large \frac{x^2}{9}+\frac{y^2}4=1\]

Answer 12

ok cool! now what do we do?

Answer 13

@terenzreignz @salehhamadeh

Answer 14

@terenzreignz 's equation is in the form I gave you. Can't you see the values of x_0, y_0, a, and b?

Answer 15

x0 and y0 are equal to zero. ie: \[x^2=(x-0)^2\]

Answer 16

and a and b are 9 and 4, respectively.

Answer 17

yeah I got that one :)

Answer 18

@alibea Sorry, the values are +/- 3 and +/- 2, respectively. They should be a^2 and b^2

Answer 19

Use the formulas on this page to determine what you're looking for: http://en.wikipedia.org/wiki/Ellipse#In_Euclidean_geometry

Answer 20

ahhhh ok I understand so i think it would be like 0,-3 0,3 right?

Answer 21

so for focus i got sqrt5 but woul that be sqrt5,0 or 0,sqrt5

Answer 22

positioning confuses me most of the time

Answer 23

You need to identify which axis is the major axis and which one is the minor axis. The major axis is the one where the ellipse appears to be more stretched, and vice versa. The foci lie sqrt(5) on the major axis.

Answer 24

I mean sqrt(5) units from the center on the major axis if this makes more sense.

Answer 25

if a > b, the x-axis is your major axis and y-axis is your minor axis. If a < b, the y-axis is your major axis. If a=b, then both axes are equal and your equation is an equation for a circle.

Answer 26

so in this case 9 is greater so the y is greater making the correct choice in this case C right?

Answer 27

@salehhamadeh @terenzreignz

Answer 28

a = 9. If a > b, x-axis is the major axis.

Answer 29

See the graph on this page http://www.mathopenref.com/coordgeneralellipse.html

Answer 30

yeah but 9 is under y^2 not x^2???

Answer 31

right?

Answer 32

9 is b

Answer 33

OHHHH YOU"RE SO RIGHT!!! nevermind!!!!! :) I'm sorry I see it now. THANK YOU!

Answer 34

answers actually A lol

Answer 35

Sorry I had to go and I forgot you were still here. Anyways, I think you get it now. Keep practicing.