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## Draw three contour for the following functions

- Asked on 17 de November, 2017
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* Graphing a function * draw three contour for the following functions 1.

## Answer

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The first is a paraboloid elliptic, where you can do:
1=x^2/(1/2)^2 + y^2; obtaining a horizontal axis of 1/2 with respect to the vertical.
[http://www.wolframalpha.com/input/?i=z%3D4x%5E2%2By%5E2](https://www.wolframalpha.com/input/?i=z%3D4x%5E2%2By%5E2)
The second is a paraboloid hyperbolic with axes in the ratio 1:1, you can write as: 1= x^2/1^2 - y^2/1^2.
[http://www.wolframalpha.com/input/?i=z%3D%3Dy%5E2%E2%88%92+x%5E2](http://www.wolframalpha.com/input/?i=z%3D%3Dy%5E2%E2%88%92+x%5E2)
The third is also a paraboloid elliptical, you can write that as:
1= 36-9x^2-4y^2; 1= 6^2 - (3x)^2 - (2y)^2;
6^2 = x^2 / (1/3)^2 + y^2 / (1/2)^2; where you can see that the relationships between the axes is 3:2.
[http://www.wolframalpha.com/input/?i=z%3D%E2%88%9A(36-9x%5E2-4y%5E2)](http://www.wolframalpha.com/input/?i=z%3D%E2%88%9A(36-9x%5E2-4y%5E2))
In the three directions of Wolfram you have the plots in R3 as the level curves.

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