- #1

Yankel

- 395

- 0

Hello all,

I have a question relating the drawing of levels curves.

The function is:

\[f(x,y)=(y-2x)^{2}\]

Fairly simple if I may add.

In order to draw the levels curves, I did:

\[(y-2x)^{2}=k\]

which resulted in:

\[y=2x\pm \sqrt{k}\]

So far so good. So for k=1, I get two straight lines, one intersecting the y-axis at -1 and one at 1. Same for every other value of k. However, when I put k=0, I get y=2x.

Drawing the levels curves in both MAPLE and Wolfram Alpha, resulted in plots in which there is no line going through the origin. My question is why ? What am I missing about k=0 ?

Thank you !

View attachment 7945

I have a question relating the drawing of levels curves.

The function is:

\[f(x,y)=(y-2x)^{2}\]

Fairly simple if I may add.

In order to draw the levels curves, I did:

\[(y-2x)^{2}=k\]

which resulted in:

\[y=2x\pm \sqrt{k}\]

So far so good. So for k=1, I get two straight lines, one intersecting the y-axis at -1 and one at 1. Same for every other value of k. However, when I put k=0, I get y=2x.

Drawing the levels curves in both MAPLE and Wolfram Alpha, resulted in plots in which there is no line going through the origin. My question is why ? What am I missing about k=0 ?

Thank you !

View attachment 7945