What does 1/2 = x^2 + xy + y^2 look like

[petrol.veem]

I'm trying to picture this in my head but can't.

What does the function 1/2 = x^2 + xy + y^2 look like?

Thanks!

 

[galactus]

I have been trying to load a graph, but it won't load. But I can tell you it is a 'sideways' ellipse.

 

[stapel]

What does the function 1/2 = x^2 + xy + y^2 look like?

Have you studied "rotation of axes" yet?

Thank you!

Eliz.

 

[petrol.veem]

Thanks galactus, that picture helps.

stapel, what are rotations of axes?

 

[stapel]

what are rotations of axes?

"Rotation of axes" is what you would use to put the given equation (with the "xy" term) into a more-familiar form (that you would have recognized as being an ellipse).

If you've never heard of this, then you probably don't need it for this assignment. :wink:

Eliz.

 

[Dr. Flim-Flam]

Note: All conics can be explicily solved for y. Hence y= (-x plus or minus square root of 2-3x^2)/2..

Graph these two equations and you will get an oblique ellipse. Since you just want to know what it

looks like, the rotation of axis isn't necessary.

 

[stapel]

Note: All conics can be explicily solved for y. Hence y= (-x plus or minus square root of 2-3x^2)/2.

Note to petrol.veem: This solving is done with the Quadratic Formula.

In your case, you would rewrite as "y[sup:h3a6dwb3]2[/sup:h3a6dwb3] + xy + (x[sup:h3a6dwb3]2[/sup:h3a6dwb3] - 1/2) = 0", and apply the Formula with a = 1, b = x, and c = x[sup:h3a6dwb3]2[/sup:h3a6dwb3] - 1/2. This will give you:

. . . . .y = ( -x +/- sqrt[2 - 3x[sup:h3a6dwb3]2[/sup:h3a6dwb3]] ) / 2

Do the graphing (in your calculator is simplest) with the first graph having the "plus square root of", and the second graph having the "minus square root of". Your calculator will likely show a small gap between the two halves, but (especially if you have the screen set to graph "square") you should be able to "see" that the connected figure would be an ellipse. :wink:

Eliz.