First slide

Equation of line in Straight lines

Question

If $α + β + γ = 0$ , the line $3 α x + β y + 2 γ = 0$ passes through the fixed point

Moderate

A

$(2, \frac{2}{3})$
B

$(\frac{2}{3}, 2)$
C

$(- 2, \frac{2}{3})$
D

None of these

Solution

The given line is $3 α x + β y + 2 γ = 0$
$\Rightarrow 3 α x + β y + 2 [- α - β] = 0 (∵ α + β + γ = 0)$
$\Rightarrow α (3 x - 2) + β (y - 2) = 0$
$\Rightarrow$ the given line passes through the point of intersection of the lines 3x – 2 = 0 and y – 2 = 0 i.e., $(\frac{2}{3}, 2)$ for all values of $α a n d β$ .

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