First slide

Equation of line in Straight lines

Question

If $u = a_{1} x + b_{1} y + c_{1}, v = a_{2} x + b_{2} y + c_{2} = 0$ and $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ then $u + k v = 0$

Moderate

A

a family of concurrent lines
B

a family of parallel lines
C

$u = 0$ or $v = 0$
D

none of these

Solution

$u = 0, v = 0$ are parallel lines but not identical . $u + k v = 0$ represents a family of lines parallel to these lines.

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