level curves

**Link88** · May 13th 2009, 06:21 PM

Sketch the level curves z = c for z = x^2/y , c=-4,-1,0,1,4

**Danny** · May 14th 2009, 04:45 AM

Originally Posted by Link88

Sketch the level curves z = c for z = x^2/y , c=-4,-1,0,1,4

The level curves are obtained by setting z =-4, -1 0 1 and 4 so we simply draw the functions

$ y = - \frac{x^2}{4},\;\; y = - x^2 \;\; y = x^2 \;\; y = \frac{x^2}{4} $

**chisigma** · May 14th 2009, 07:10 AM

Setting c equal to -4,-1,1,4 we obtain...

$y= - \frac{x^{2}}{4}, y= - x^{2}, y= x^{2}, y= \frac{x^{2}}{4}$

... good!

... and setting, as also requested, c=0?

...

Kind regards

$\chi$ $\sigma$

**chisigma** · May 14th 2009, 11:09 PM

Thanks are undeserved since my observations were quite obvious... also quite obvious is that the level curve for $c=0$ is $x=0$ , i.e. the level curve is the y-axis...

Kind regards

$\chi$ $\sigma$

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