Graph 4x^2 + y^2 = 9. What are its lines of symmetry?

Question

mertsj · Answer

Do you recognize that this is an ellipse?

anonymous · Answer

no I did not please explain.. :)

mertsj · Answer

This is one of those situations that arise in mathematics when you have to recognize when there is something to reason out and when there is something to learn.  This time there is something to learn.  You must learn to recognize the conic sections by looking at their equations.

mertsj · Answer

I will try to help you.

anonymous · Answer

Ok would you like the multiple choice answers?

mertsj · Answer

In a circle, you must have x^2 and y^2.  The signs must be positive and the coefficients must be the same.

mertsj · Answer

In a parabola, you must have x and y^2 or y and x^2.  Then you know the graph is a parabola.

mertsj · Answer

In an ellipse you must have x^2 and y^2, both positive but the coefficients are not the same.

mertsj · Answer

In a hyperbola, you must have x^2 and y^2 but one of them is negative.

anonymous · Answer

attachment

mertsj · Answer

So now we know that 4x^2 + y^2 = 9 is an ellipse because we have x^2 and y^2.  Both are positive and the coefficients are different.

anonymous · Answer

ok.

mertsj · Answer

So now your job is to rearrange it so it is in this form:
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

mertsj · Answer

Let me know when you have that done.

anonymous · Answer

umm ok well im not completely sure of how to rearange i t

mertsj · Answer

Do you notice that the right side has to be 1?

anonymous · Answer

ah yes

mertsj · Answer

What is the right side of your equation?

anonymous · Answer

the one?

mertsj · Answer

Here is your problem:

4x^2 + y^2 = 9

What is the right side?

anonymous · Answer

ok the 9

mertsj · Answer

But it is supposed to be 1.  So you must answer the question, "What should I do to the 9 to turn it into a 1?"

anonymous · Answer

Divide by 9? Im just a little confused.

mertsj · Answer

Yes.  Excellent!!  Divide by 9.  Divide EVERY term on BOTH sides by 9.

Post your result.

anonymous · Answer

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

mertsj · Answer

Yes.  Perfect.  Now remember, we want it to be in the form:
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
and we have it in the form:
$$\frac{4x^2}{9}+\frac{y^2}{9}=1$$

mertsj · Answer

So we are not quite there.

mertsj · Answer

Do you know that multiplying by 4/9 is the same as dividing by 9/4?

anonymous · Answer

so it would be 
4x^2               y^2 
------    + -----------
9x^2               9^2

mertsj · Answer

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