Understanding Homogeneous Equations in Coordinate Geometry

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Homogenizing an equation in coordinate geometry refers to transforming it into a form where it equals zero, such as changing "ax + by = c" to "ax + by = 0." This process allows for the analysis of lines and their relationships in a more standardized way. The original equation represents a line intersecting the axes, while the homogeneous form represents a line through the origin, maintaining parallelism. Understanding this concept is crucial for solving geometric problems and analyzing linear relationships. Homogeneous equations play a significant role in simplifying and solving various geometric scenarios.
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Can anyone please explain to me what is meant by homogenizing an equation in context of coordinate geometry and when to use it?
 
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Yatin said:
Can anyone please explain to me what is meant by homogenizing an equation in context of coordinate geometry and when to use it?
Do you have a reference or citation which provides more information about your question?
 
Generally, a "homogeneous" equation is one that is equal to 0. In "coordinate geometry" I would think it means changing an equation from, say, "ax+ by= c" to "ax+ by= 0". The graph of the first is a line passing through (c/a, 0) and (0, c/b) and the graph of the second is a line parallel to that through (0, 0).
 
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