Which statements are true?

I

iamtoostinky

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Nov 21, 2005
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Consider the ellipse
x^2/4 + y^2/9 = 1 and the circle
x^2 + y^2 = 36.
Which of the following statements is true?

I.The circle is contained inside the ellipse.
II. The ellipse is contained inside the circle.
III. The circle and the ellipse intersect.
IV. None of these is true
 
My earlier question was meant to hint that graphing would provide a quick solution.

The graph of the circle, being centered at the origin and having a nice whole-number radius, is easy to do. The graph of the ellipse, being centered at the origin and having nice whole-number vertices, is fairly straightforward to sketch. (You don't have to be very exacting about this; just rough it out.)

When you do the graphs, the answer should be immediately obvious.

Eliz.
 
It might help if you described the graph you're looking at. It seems difficult to me to draw an ellipse that goes no further than (0, -3) to (0, 3) and have it somehow intersect with a circle that crosses at (0, -6) and (0, 6).

On a personal note, please know that I didn't mean to upset you by providing hints and explanations so you could figure out the solution on your own by understand the concepts. Perhaps the poster who gives just the answers will be along shortly.

In the meanwhile, however, it might be helpful if you let us know what you are doing, so we can try to figure out what the difficulty is. Otherwise, it will be possible to have the exact same problem when you encounter the next exercise of this type.

Again, I apologize for having frightened or otherwise distressed you.

Eliz.
 
iamtoostinky said:
Consider the ellipse
x^2/4 + y^2/9 = 1 and the circle
x^2 + y^2 = 36.
Which of the following statements is true?

I.The circle is contained inside the ellipse.
II. The ellipse is contained inside the circle.
III. The circle and the ellipse intersect.
IV. None of these is true
Click to expand...

the circle has centre (0,0) and radius 6
the ellipse has centre (0,0) also and is 2 wide in the x-direction and 3 in the y.
so therefore only the first one is true
 
mad_mathematician said:
the circle has centre (0,0) and radius 6
the ellipse has centre (0,0) also and is 2 wide in the x-direction and 3 in the y.
so therefore only the first one [The circle is contained inside the ellipse.] is true
Click to expand...
You are correct regarding the locations of the circle and the ellipse, but how did you come to the conclusion that the smaller ellipse surrounds the larger circle?

Eliz.
 
mad_mathematician said:
iamtoostinky said:
Consider the ellipse
x^2/4 + y^2/9 = 1 and the circle
x^2 + y^2 = 36.
Which of the following statements is true?

I.The circle is contained inside the ellipse.
II. The ellipse is contained inside the circle.
III. The circle and the ellipse intersect.
IV. None of these is true
Click to expand...

the circle has centre (0,0) and radius 6
the ellipse has centre (0,0) also and is 2 wide in the x-direction and 3 in the y.
so therefore only the first one is true
Click to expand...

sorry, my mistake, what i meant to say was that the ellipse is entirely inside the circle, ie the second one is the only true one
 
Just a thought...Maybe you should consider a new screen name and a new attitude to go with it. You cannot NEED to talk about yourself like that. Let's upgrade it a bit. :)
 
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