- #1
Yankel
- 390
- 0
Hello all,
I need your assistance with the following:
Find the equation of the line that goes through the origin (0,0) if it is known that the sum of distances of the line from A(2,1) and B(1,4) is equal to \[\sqrt{8}\], and it is also known that the line is between the points.
The formula I am supposed to use is:
\[d=\frac{\left | Ax+By+C \right |}{\sqrt{A^{2}+B^{2}}}\]
What I did, is I set the equation to be:
\[\frac{-2A-B-C}{\sqrt{A^{2}+B^{2}}}+\frac{A+4B+C}{\sqrt{A^{2}+B^{2}}}=\sqrt{8}\]
The absolute value was omitted since the line is between the points, i.e. one point is below and one above.
I am stuck with 1 equation and 2 variables. How do I proceed ? Since the point (0,0) is on the line, I know that C is 0 in the equation Ax+By+C=0, but this parameter is not important anyway (C-C=0).
Thank you !
I need your assistance with the following:
Find the equation of the line that goes through the origin (0,0) if it is known that the sum of distances of the line from A(2,1) and B(1,4) is equal to \[\sqrt{8}\], and it is also known that the line is between the points.
The formula I am supposed to use is:
\[d=\frac{\left | Ax+By+C \right |}{\sqrt{A^{2}+B^{2}}}\]
What I did, is I set the equation to be:
\[\frac{-2A-B-C}{\sqrt{A^{2}+B^{2}}}+\frac{A+4B+C}{\sqrt{A^{2}+B^{2}}}=\sqrt{8}\]
The absolute value was omitted since the line is between the points, i.e. one point is below and one above.
I am stuck with 1 equation and 2 variables. How do I proceed ? Since the point (0,0) is on the line, I know that C is 0 in the equation Ax+By+C=0, but this parameter is not important anyway (C-C=0).
Thank you !