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How to obtain the following equality relationship?

Posted 24 days ago

In the code below, the parameters l1 and l2 represent the same straight line. How can I use code to obtain the following equality relationship?

m == x0/(x0^2 + y0^2)
n == y0/(x0^2 + y0^2)

enter image description here

I used the following code but it didn't achieve the intended purpose.

l1 = (y - y0) == -x0/y0 (x - x0)
l2 = m x + n y == 1
Solve[ForAll[{x, y}, Subtract @@ l1 == Subtract @@ l2]]
POSTED BY: Wen Dao
2 Replies

This is a way:

Solve[ForAll[{x, y}, Equivalent[l1, l2]], {n, m}]
POSTED BY: Gianluca Gorni
Posted 23 days ago

Thank you!

Also:

Solve[ForAll[{x, y}, l1, l2], {n, m}]
POSTED BY: Updating Name
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