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Question
Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.
Solution
Line Ax + By + C = 0
or y = `-"A"/"B" "x" - "C"/"B"`
Slope of line = `-"A"/"B"`
∴ Slope of parallel line = `-"A"/"B"`
The equation of the parallel line passing through (x1, y1)
`"y" - "y"_1 = -"A"/"B"("x" - "x"_1)`
`"B"("y" - "y"_1) = -"A"("x" - "x"_1)`
A(x − x1) + B(y − y1) = 0
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