First slide

Equation of line in Straight lines

Question

The number of possible straight lines, passing through (2, 3) and forming a triangle with co-ordinate axes, whose area is 12 sq. units is

Moderate

A

1
B

2
C

3
D

4

Solution

$Equation of line \frac{x}{a} + \frac{y}{b} = 1, through (2, 3)$
$\begin{aligned} \Rightarrow \frac{2}{a} + \frac{3}{b} = 1 \Rightarrow 2 b + 3 a = a b \\ \begin{array}{l} area = \frac{1}{2} | a b | = 12 \\ | a b | = 24 \Rightarrow a b = \pm 24 \\ When a b = 24 \\ 2 b + 3 a = 24 \end{array} \end{aligned}$
$\begin{aligned} \Rightarrow 2 a b + 3 a^{2} = 24 a \\ \Rightarrow 3 a^{2} - 24 a + 48 = 0 \\ \Rightarrow a^{2} - 8 a + 16 = 0 \\ \Rightarrow a = 4 \Rightarrow b = 6 \\ When a b = - 24 \\ \Rightarrow 2 b + 3 a = - 24 \\ \Rightarrow a^{2} + 8 a - 16 = 0 \end{aligned}$
Two values of a. Hence 3 straight lines.

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