Homework Help: Rally easy question (but I still need help)

1. Feb 21, 2006

mmh37

I am trying to draw the contour plot of the following function:

$$f(x,y) = \frac {a(x+y)} {x^2 + y^2 + a^2}$$

by setting h(x,y) = 1 and completing the square I recieved the following:

$$(x-(a/2))^2 - (y-a/2)^2 = a^2$$

surely, this is not a circle, and not a ellipse...but what is it then.

Also, is there a possibility to draw contour plots rather fast (e.g. with Mathcad)?

2. Feb 21, 2006

quasar987

Hyperboleas are caracterised by the implicit relation

$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

3. Feb 21, 2006

mmh37

but I thought there would be a + in between the square brackets in order for it to be a circle, i.e.

$$(x-(a/2))^2 + (y-a/2)^2 = a^2$$

or does it simply not matter?

4. Feb 21, 2006

quasar987

You read my post before I could delete it. I had missed the - sign and though you were confused about the a/2 translation.

See my new post.

5. Feb 21, 2006

assyrian_77

You can draw contour plots in Mathematica.

6. Feb 21, 2006

mmh37

Thank you very much! The entire thing does make so much more sense now! :-)

So, is a/2 the focal point then (i.e. where the asymptotes cross)?

7. Feb 21, 2006

quasar987

a/2 is still a translation. the assymptotes are y=±bx/a

8. Feb 21, 2006

mmh37

Thanks a lot! It's much appreciated!