SOLUTION: PLEASE HELP. WHAT IS THE EQUATION OF A LINE THROUGH (4, -1) AND WHOSE SEGMENT INTERCEPTED BETWEEN THE AXES IN THE 4TH QUADRANT IS EQUAL TO {{{ 2sqrt(17) }}}. THANKS IN ADVANCE.

Question 875156: PLEASE HELP. WHAT IS THE EQUATION OF A LINE THROUGH (4, -1) AND WHOSE SEGMENT INTERCEPTED BETWEEN THE AXES IN THE 4TH QUADRANT IS EQUAL TO . THANKS IN ADVANCE.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
DISCLAIMER:
The solution that follows is not elegant.
I would welcome any alternative.
If this strategy was the expected one, and maybe there is no better way, I would love to know that too.

The situation in the problem is illustrated in the drawing below.
We are looking for and the coordinates of and of A and B,
and all of them should be negative.
We use <---> to find and as a function of .
---> --->
---> --->
Since <--><-->
and ,

Substituting and we get

There are 4 real solutions to that equation, and we can find their approximate values. I suppose that using a graphing calculator was expected, but I used the computer, since I am already using it to access the answer this question.
The solution we are interested in is the one with
,
because that would give us .
That solution is ,
which makes ,
so the equation of the line is

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