anonymous
  • anonymous
Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@salehhamadeh
terenzreignz
  • terenzreignz
Can you get it to look like this: \[\Large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]
anonymous
  • anonymous
these are the answer choices btw.
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anonymous
  • anonymous
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: \[(x-x_0)^2/a + (y-y_0)^2/b = 1\]
anonymous
  • anonymous
ok let me try it!
anonymous
  • anonymous
The center will be (x0, y0)
anonymous
  • anonymous
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.
anonymous
  • anonymous
ok I'm having a bit of trouble getting it into that form
anonymous
  • anonymous
Where are you getting stuck?
anonymous
  • anonymous
1x^2/9+1y^2/4=1?
terenzreignz
  • terenzreignz
That's good. You can do away with those 1's... \[\Large \frac{x^2}{9}+\frac{y^2}4=1\]
anonymous
  • anonymous
ok cool! now what do we do?
anonymous
  • anonymous
@terenzreignz @salehhamadeh
anonymous
  • anonymous
@terenzreignz 's equation is in the form I gave you. Can't you see the values of x_0, y_0, a, and b?
anonymous
  • anonymous
x0 and y0 are equal to zero. ie: \[x^2=(x-0)^2\]
anonymous
  • anonymous
and a and b are 9 and 4, respectively.
anonymous
  • anonymous
yeah I got that one :)
anonymous
  • anonymous
@alibea Sorry, the values are +/- 3 and +/- 2, respectively. They should be a^2 and b^2
anonymous
  • anonymous
Use the formulas on this page to determine what you're looking for: http://en.wikipedia.org/wiki/Ellipse#In_Euclidean_geometry
anonymous
  • anonymous
ahhhh ok I understand so i think it would be like 0,-3 0,3 right?
anonymous
  • anonymous
so for focus i got sqrt5 but woul that be sqrt5,0 or 0,sqrt5
anonymous
  • anonymous
positioning confuses me most of the time
anonymous
  • anonymous
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.
anonymous
  • anonymous
I mean sqrt(5) units from the center on the major axis if this makes more sense.
anonymous
  • anonymous
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.
anonymous
  • anonymous
so in this case 9 is greater so the y is greater making the correct choice in this case C right?
anonymous
  • anonymous
@salehhamadeh @terenzreignz
anonymous
  • anonymous
a = 9. If a > b, x-axis is the major axis.
anonymous
  • anonymous
See the graph on this page http://www.mathopenref.com/coordgeneralellipse.html
anonymous
  • anonymous
yeah but 9 is under y^2 not x^2???
anonymous
  • anonymous
right?
anonymous
  • anonymous
9 is b
anonymous
  • anonymous
OHHHH YOU"RE SO RIGHT!!! nevermind!!!!! :) I'm sorry I see it now. THANK YOU!
anonymous
  • anonymous
answers actually A lol
anonymous
  • anonymous
Sorry I had to go and I forgot you were still here. Anyways, I think you get it now. Keep practicing.

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