construct a function whose level curves are lines passing through the origin.

i don't know how to express this function...can anyone help? is the center have to be 0,0 but i don't know how to write this...

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- Jul 6th 2008, 07:50 PMchris25level curves
construct a function whose level curves are lines passing through the origin.

i don't know how to express this function...can anyone help? is the center have to be 0,0 but i don't know how to write this... - Jul 6th 2008, 09:45 PMmr fantastic
- Jul 8th 2008, 10:21 AMMathstud28
Maybe I am misunderstanding the question, but isn't the OP looking for a function such that $\displaystyle f(x,y)=c$ is linear and passes through the origin? So if your function was correct we would have that

$\displaystyle cx^2+cy^2=2xy$ which is not even a function let alone one that is linear. - Jul 8th 2008, 02:31 PMmr fantastic
Solve $\displaystyle cy^2 - 2xy + cx^2 = 0$ using the quadratic formula. You get solutions of the form y = mx where m is a function of c. There is only a certain set of values of c for which these lines exist. No level curves exist for values of c lying outside of these values.

Note: c = 0 gives the level curves x = 0 and y = 0 (which obviously pass through the origin).

Clearly this example is one of an infinite number of possibilities. I can only hope the OP has not been discouraged from contemplating it as a solution to his/her problem. - Jul 8th 2008, 06:57 PMmr fantastic
Of relevance is the general Cartesian equation of a conic,

*viz*.

$\displaystyle ax^2 + 2{\color{red}c}xy + {\color{red}b}y^2 + 2dx + 2ey + f = 0$.

(I have switched the standard notation slightly [see red] to be consistent with the example I gave).

It defines a hyperbola, a parabola, an ellipse, a circle or a**pair of lines**depending on the value of the invariants of the curve.

A little bit of research should show origins of the example I gave. - Jul 9th 2008, 06:07 AMjme44Answer
I know there can be many different answers. But what exactly do you do to go about getting one.

is F(x,y) = 2x +3y - Jul 9th 2008, 02:36 PMmr fantastic