- #1

daniel_i_l

Gold Member

- 867

- 0

I read this question a few days ago:

Lets say that you have a line that goes from a point on the +y axis to a point on the +x axis with the length of L. There's an infinate amount of such lines, starting with a line that goes from (0,0) to (0,L) and ending with one that goes form (0,0) to (L,0). Now the question is, what function describes the envelope of all of those lines?

I got:

y(x) = sqrt(L^2 - (L^2 * x)^2/3)x / (L^2 * x)^1/3 + sqrt(L^2 - (L^2 * x)^2/3)

Can anyone verify that?

Thanks.

EDIT: i changed the equation a little

Lets say that you have a line that goes from a point on the +y axis to a point on the +x axis with the length of L. There's an infinate amount of such lines, starting with a line that goes from (0,0) to (0,L) and ending with one that goes form (0,0) to (L,0). Now the question is, what function describes the envelope of all of those lines?

I got:

y(x) = sqrt(L^2 - (L^2 * x)^2/3)x / (L^2 * x)^1/3 + sqrt(L^2 - (L^2 * x)^2/3)

Can anyone verify that?

Thanks.

EDIT: i changed the equation a little

Last edited: