Question

The equation of the line, when the portion of it intercepted between the axes is divided by the point $(2,3)$ in the ratio of $3:2$, is

• A. Either $x+y=4$ or $9x+y=12$
• B. Either $x+y=5$ or $4x+9y=30$
• C. Either $x+y=4$ or $x+9y=12$
• D. Either $x+y=5$ or $9x+4y=30$

Answer 1

Answer: (B)

Either $x+y=5$ or $4x+9y=30$

Now $\frac{2a}{5}=2\Rightarrow a=5$

$\frac{3b}{5}=3\Rightarrow b=5$

Therefore equation of the line is $\frac{x}{5}+\frac{y}{5}=1\Rightarrow x+y=5$.

Now $\frac{3a}{5}=2\Rightarrow a=\frac{10}{3}$

$\frac{2b}{5}=3\Rightarrow b=\frac{15}{2}$

Therefore equation of the line is $\frac{x}{10/3}+\frac{y}{15/2}=1$.

$\Rightarrow \frac{3x}{10}+\frac{2y}{15}=1$

$\Rightarrow 9x+4y=30$

Hence the equation of the line is $x+y=5$ or $9x+4y=30$.