First slide

Equation of line in Straight lines

Question

If the point $(a, b)$ divides a line between the axes in the ratio $2 : 3$ , the equation of the line is

Moderate

A

$a x + b y = 5$
B

$b x + a y = 5$
C

$\frac{2 x}{a} + \frac{3 y}{b} = 5$
D

$2 a x + 3 b y = 5$

Solution

Let the line meet $x -$ axis at $(h, 0)$ and $y -$ axis at $(o, k)$ , then the equation of the line is $\frac{x}{h} + \frac{y}{k} = 1$
(Intercept form)
Since $P (a, b)$ divides $B A$ in the ratio $2 : 3$ we get
$\frac{2 h + 0 \times 3}{5} = a, \frac{2 \times 0 + 3 k}{5} = b$
$\Rightarrow h = \frac{5 a}{2}, k = \frac{5 b}{3}$ and the required equation is $\frac{2 x}{a} + \frac{3 y}{b} = 5$

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