NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 45

Total: 74

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:

Given equation of a line is Ax + By + C = 0
∴ Slope of the above line = −

i.e. slope of any line parallel to given line and passing through (x1,y1) is −

then equation is (y−y1) = −

(x−x1)
⇒ B(y–y1) = –A(x–x1) ⇒ A(x–x1)+B(y–y1) = 0.
Hence proved.

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