Question: Find the single equation represented by the following pair of straight lines: ax = by, and by - ax = 0.


Solution:
Given,

Equation of line i is ax = by
or, ax - by = 0

Equation of line ii is by - ax = 0

Now,

Multiplying equation i and ii, we get,

(ax - by)(by - ax) = 0

or, ax(by - ax) - by(by - ax) = 0

or, abxy - a²x² - b²y² + abxy = 0

or, -a²x² - b²y² + 2abxy = 0

or, a²x² - 2abxy + b²y² = 0

Hence, a²x² - 2abxy + b²y² = 0 is the required single equation of the given pair of lines.


Related Notes and Solutions:

Here is the website link to all the important formulae of Coordinate Geometry of Class 10.

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