Coordinate Geometry: Find A & B on 5x-12y=6 & 3x-4y=-2

AI Thread Summary
The problem involves finding points A and B on the line defined by the equation 5x-12y=6, with each point having a perpendicular distance of 4 units from the line 3x-4y=-2. A is located on the same side of the second line as the origin, while B is on the opposite side. The confusion arises from the relationship between the two lines and the positioning of points A and B relative to the origin. To solve the problem, one must determine the coordinates of A and B that satisfy these conditions. The discussion highlights the need for clarity in understanding the geometric relationships between the lines and the points.
thereddevils
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Homework Statement



The points A and B are located on the line 5x-12y=6.The perpendicular distances of A and B respectively from the line 3x-4y=-2 are both 4 units. A lies on the same side of 3x-4y=-2 as the origin ,and B lies on the other side. Find the coordinates of A and B.

Homework Equations





The Attempt at a Solution



I do not understand what it means by the line in red. It has been previously stated both A and B lies on the same line so now how can they be on different sides relative to the origin?
 
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A and B lie on the first line, but on each side of the second line.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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