Question

The equation of the straight line which passes through the point $(-5,4)$ and is such that the portion of it between the axes is divided by the given point in the ratio $1:2$ is :

• A. $\frac{x}{12}+\frac{y}{-\frac{15}{2}}=1$
• B. $\frac{x}{-\frac{15}{2}}+\frac{y}{12}=1$
• C. $\frac{x}{12}+\frac{y}{\frac{15}{2}}=1$
• D. None of these

Answer 1

The correct option is B $\frac{x}{-\frac{15}{2}}+\frac{y}{12}=1$

We know that the equation of a line making intercept $a$ and $b$ on the x-axis and y-axis respectively is given by
$\frac{x}{a}+\frac{y}{b}=1$ ...(1)
Let the line intersect the x-axis at A and y-axis at B as shown in figure .Let point $C(-5,4)$ lies on the line AB and divides it in ration $1:2$
Therefore by section formulae, we have
$\frac{1.0+2.a}{1+2}=-5$ and
$\Rightarrow \frac{0+2a}{3}=-5$ and $\frac{b+0}{3}=4$
$\Rightarrow 2a=-15$ and $b=12$
$\Rightarrow a=-\frac{15}{2}$ and $b=12$
Therefore from (1), we have
$\frac{x}{-\frac{15}{2}}+\frac{y}{12}=1$