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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 45 of 74
Marks: +1, -0
Prove that the line through the point (x1,y1)(x_1, y_1) and parallel to the line Ax + By + C = 0 is A(x−x1)+B(y−y1)A(x - x_1) + B(y - y_1) = 0.
Solution:  
Given equation of a line is Ax + By + C = 0
∴ Slope of the above line = −A/B-A/B
i.e. slope of any line parallel to given line and passing through (x1,y1)(x_1,y_1) is −A/B-A/B
then equation is (y−y1)(y-y_1) = −A/B(x−x1)-A/B (x-x_1)
⇒ B(y−y1)B(y - y_1) = −A(x−x1)-A(x - x_1) ⇒ A(x−x1)+B(y−y1)A(x - x_1) + B (y - y_1) = 0.
Hence proved.
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