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Question
Find the equation of the straight lines passing through the following pair of point :
(a, b) and (a + b, a − b)
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Solution
(a, b) and (a + b, a − b)
\[\text { Here }, \left( x_1 , y_1 \right) \equiv \left( a, b \right) \]
\[\left( x_2 , y_2 \right) \equiv \left( a + b, a - b \right)\]
So, the equation of the line passing through the two points is
\[y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left( x - x_1 \right)\]
\[ \Rightarrow y - b = \frac{a - b - b}{a + b - a}\left( x - a \right)\]
\[ \Rightarrow by - b^2 = \left( a - 2b \right)x - a^2 + 2ab\]
\[ \Rightarrow \left( a - 2b \right)x - by + b^2 + 2ab - a^2 = 0\]
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