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Family of lines is a set of those lines passing through the intersection of two given lines<br /> i.e., α<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub> = 0 and α<sub>2</sub>x + b<sub>2</sub>y + c<sub>2</sub> = 0 which is given by the equation. (α<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub>) + λ (α<sub>2</sub>x + b<sub>2</sub>y + c<sub>2</sub>) = 0 and any line which is parallel to a given line αx + by + c = 0 can be represented by αx + by + k =0.
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