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, 08:50 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, 10:45 PMmr fantastic
- Jul 8th 2008, 11:21 AMMathstud28
- Jul 8th 2008, 03:31 PMmr fantastic
Solve 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, 07:57 PMmr fantastic
Of relevance is the general Cartesian equation of a conic,

*viz*.

.

(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, 07:07 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, 03:36 PMmr fantastic