Q. 45

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Prove that the line through the point (x_{1},y_{1}) and parallel to the line Ax+By+C=0 is A(x-x_{1})+b(y-y_{1}) = 0

Answer :

Any line parallel to Ax+By+C = 0 is Ax+By+K=0 – (1)

Now, (x_{1},y_{1}) lies on it.

Therefore Ax_{1}+By_{1}+k=0 – (2)

From (1) and (2)

Ax+By = Ax_{1}+By_{1 }

A(x-x_{1})+B(y-y_{1})=0 (Required equation)

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