Question

The equation of straight passes through the point (-3,5) such that the portion of it between the axes is divided by the the ratio 5:3 internally (reckoning from x-axis ) will be -

• A. x + y+z = 0
• B. 2x + y +1 = 0
• C. x + 2 y - 7 = 0
• D. x - y+8 =0

Answer 1

The correct option is D x - y+8 =0

Let the equation of the line be $\frac{x}{a}+\frac{y}{b}=1$. This line meets the coordinate axes at $A(a,0)$ and $B(0,b)$ resp.

The coordinates of the point which divides the line joining $A(a,0)$ and $B(0,b)$ in the ratio $5:3$ are $[\frac{5\times \left(0\right)+3\left(a\right)}{5+3},\frac{5\times \left(0\right)+3\left(0\right)}{5+3}]$

i.e, the coordinates are,

$\Rightarrow \frac{3a}{8},\frac{5b}{8}$

It is given that the point $(-3,5)$ divides $AB$ in the ratio $5:3$

$\therefore \frac{3a}{8}=-3,\Rightarrow a=\frac{-3\times 8}{3}=-8$

and $\frac{5b}{8}=5\Rightarrow b=\frac{8\times 5}{5}=8$

hence the equation of the line is,

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

$\frac{x}{-8}+\frac{y}{8}=1$

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