Question

If the intercept of line between coordinate axes is divided by the point $(-5,4)$ in the ratio $1:2,$ then its equation is

• A. $5x-8y+60=0$
• B. $8x-5y+60=0$
• C. $2x-5y+30=0$
• D. none of these

Answer 1

The correct option is B $8x-5y+60=0$

According to Section Formula

$x=\frac{m{x}_2+n{x}_1}{m+n}y=\frac{m{y}_2+n{y}_1}{m+n}$

where, (x,y) is the point which divides the line made by the points in m:n ratio

Also,

Let the y intercept will have coordinate $(0,y)$

and the x intercept will have coordinate $(x,0)$

Hence,

$-5=\frac{2x+1\ast 0}{1+2}=\frac{2x}{3}\Rightarrow x=-\frac{15}{2}4=\frac{y+2\ast 0}{1+2}=\frac{y}{3}\Rightarrow y=12$

Now, we can write the intercept of the line as

$\frac{x}{\frac{-15}{2}}+\frac{y}{12}=1\Rightarrow \frac{-2x}{15}+\frac{y}{12}=1$

Multiplying both sides by 60

$-8x+5y=60\Rightarrow 8x-5y+60=0$