What does the graph of 9-9x^y-y^2

Question

What does the graph of 9-9x^y-y^2<0 look like, and how would I graph it on paper?

tkhunny · Answer

Well, if it were an equation, you COULD solve it for x.

anonymous · Answer

Right, I'm just having trouble visualizing what the graph of this is.

tkhunny · Answer

However, once you do that, you will have an exponent problem that will confuse most any drawing software.

This may be your opportunity to divorce yourself from the perceived need to visualize it.  Can we think it through, just from the algebra?

anonymous · Answer

I need to be able to draw it as part of my homework assignment.  I know that it will be an ellipse by looking at its form, but just not sure where to go from there on how to draw it.

tkhunny · Answer

$x^{y}$ That's an ellipse only if you wrote it in error.

tkhunny · Answer

Is it $x^{2}$

anonymous · Answer

Yes it is.  I apologize for the error.  Thanks for correcting me

anonymous · Answer

I believe it is an ellipse with vertices at (0,3) and (0,-3).  For x, there would be vertical asymptotes at (-1,0) and (1,0)

anonymous · Answer

The ellipse could get infinitely close to (-1,0) and (1,0) but just never touch it correct?

anonymous · Answer

multiply everything by $-1$ will make your life much easier

tkhunny · Answer

Oh, well that it MUCH easier.

$9x^{2} + y^{2} = 9\;or\;x^{2} + \dfrac{y^{2}}{9} = 1$

This is a vertically oriented ellipse.  Just like you have it.

No we ask ourselves just one question.  Is $9x^{2} + y^{2} > 9$, the inside or the outside of the ellipse?

anonymous · Answer

Inside.  So when I draw it, would the vertices be at (0, -3) and (0, 3) and the other vertices (whatever the are called) be at (-1, 0) and (1,0)?  The inside is the domain, but the boundary of the ellipse would not be in the domain? Sound right?

tkhunny · Answer

Check an obvious point to make sure.  (0,0) seems easy enough.  Is that in the region or not?

anonymous · Answer

Sure is.  I think our work here is done.  I really appreciate the help.

tkhunny · Answer

??

$9 - 9x^{2} - y^{2} < 0$

Try (0,0)

$9 < 0$?

That is NOT in the region.  How did you conclude that it is?

anonymous · Answer

I think I made another typing error.  The inequality should be $$9-9x^2-y^2>0$$

anonymous · Answer

Now, (0,0) works.

anonymous · Answer

Thanks for baring with me

tkhunny · Answer

{sigh}  Kind of a poor typing effort.  Do better.  Don't let communication problems get in the way of your math education.

Good work - eventually!  :-)