First slide

Equation of line in Straight lines

Question

If a, b, c are in A.P., then $a x + b y + c = 0$ represents

Moderate

A

a single line
B

a family of concurrent lines
C

a family of parallel lines
D

none of these

Solution

$\begin{array}{l} a x + \frac{(a + c)}{2} y + c = 0 \\ a (2 x + y) + c (y + 2) = 0 \end{array}$
which represents a family of lines passing through the intersection of $2 x + y = 0$ and $y + 2 = 0$

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