What type of conic section is given by the equation 4x^2+ 9y^2 = 36? What are its domain and range?

Question

zzr0ck3r · Answer

well the 4 and 9 tell us its not what?

anonymous · Answer

No idea.

zzr0ck3r · Answer

what is this graph x^2 + y^2 = 1?

anonymous · Answer

not a circle :P

anonymous · Answer

A circle?

zzr0ck3r · Answer

its not a circle, its close. what is close to a circle?

zzr0ck3r · Answer

http://www.wolframalpha.com/input/?i=4x%5E2%2B+9y%5E2+%3D+36

anonymous · Answer

zzr0ck, isnt x^2+y^2=1 a cirlce with center 0,0 and radius 1?

zzr0ck3r · Answer

yes

anonymous · Answer

Oh. So its an ellipse.

zzr0ck3r · Answer

so what would happen if we did 4x^2 + 9x^2 = 1

zzr0ck3r · Answer

yes @xkylex

anonymous · Answer

It would be a circle

anonymous · Answer

$$4x^2+ 9y^2 = 36$$$${4x^2\over36}+{9y^2\over36}={36\over36}$$$${x^2\over9}+{y^2\over4}=1$$
$${x^2\over a^2}+{y^2\over b^2}=1~~is~~an~~ellipse$$ :)

anonymous · Answer

zzr0ck that would be an ellipse, but what does the 4 and 9 mean exactly?

zzr0ck3r · Answer

that is what is stretching it

anonymous · Answer

@_@, im so confused.

zzr0ck3r · Answer

a circle is 1*x^2 + 1*y^2 = 1

anonymous · Answer

so it stretches it how much?

zzr0ck3r · Answer

when we change the ones it changes

zzr0ck3r · Answer

that's a hard question, for calculus

anonymous · Answer

So how would I find the domain and range?

anonymous · Answer

zzrock if you look at the graph of an ellipse, how can you make the equation from just looking at it??

zzr0ck3r · Answer

you can get points and solve the equation yummy posted, they always have the same form

anonymous · Answer

well technically you have to put it into the form of an equation of an ellipse before you graph it...the graph would look like this:|dw:1369973189718:dw|

anonymous · Answer

OH!

anonymous · Answer

The domain would be -3, 3. 

The range would be -2 2.

anonymous · Answer

Is that right?

anonymous · Answer

the domain would be $[-3,3]$ and the range would be $[-2,2]$

anonymous · Answer

Thank you everyone!
If only I could give more than one medal :c .

anonymous · Answer

$$a=3$$$$b=2$$$$c=\sqrt{5}$$$$focus:(-\sqrt{5},0)~~and~~(\sqrt{5},0}$$

zzr0ck3r · Answer

strange question, this is not a function and thus to talk about its domain and range is pointless...

anonymous · Answer

true, domain and range is pointless, I agree