First slide

Equation of line in Straight lines

Question

Lines $a x + b y + c = 0$ and $3 a + 2 b + 4 c = 0$ $a, b, c \in R$ are concurrent at the point.

Moderate

A

(3, 2)
B

(2, 4)
C

(3, 4)
D

(3/4, 1/2)

Solution

$3 a + 2 b + 4 c = 0$
$\Rightarrow \frac{3}{4} a + \frac{1}{2} b + c = 0$
$\Rightarrow a x + b y + c$ passes through (3/4, 1/2) for all values of $a, b, c .$

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