Question

The equation of the line which passes through the point $(3,4)$ and the sum of its intercept on the axes is $14$ is :

• A. $4x-3y=24,x-y=7$
• B. $4x+3y=24,x+y=7$
• C. $4x+3y+24=0,x+y+7=0$
• D. $4x-3y+24=0,x-y+7=0$

Answer 1

The correct option is B $4x+3y=24,x+y=7$

Let the equation of the required line be

$\frac{x}{a}+\frac{y}{b}=1$

$a+b=14$ (Given)

$\Rightarrow b=14-a$

So the equation of the line:

$\frac{x}{a}+\frac{y}{14-a}=1$

If passes through $(3,4)$

$\frac{3}{a}+\frac{4}{14-a}=1$

$\Rightarrow a^2-13a+42=0$

$\Rightarrow a-6a-7a+42=0$

$\Rightarrow a(a-6)-7(a-6)=0$

$\Rightarrow (a-6)(a-7)=0$

$a=6,7$

When $a=6$, required line is $\frac{x}{6}+\frac{y}{8}=1\Rightarrow \frac{4x+3y=1}{24}$

$\Rightarrow 4x+3y=24$

$\Rightarrow 4x+3y-24=0$

When $a=7$ required lien is $\frac{x}{7}+\frac{y}{7}\Rightarrow \frac{x+y}{7}=1\Rightarrow x+y=7$

$\Rightarrow x+y-7=0$