Question

The equation straight line is such that it passes through point $(-2,6)$ and the portion of the line intercepted between the axes is divided at this point in the ratio $3:2$ is :

• A. $2x-9y=10$
• B. $9x-2y+30=0$
• C. $9x-2y=10$
• D. $x+2y=10$

Answer 1

Answer: (B)

$9x-2y+30=0$

Let the required line intercept the y-axis at $Y(0,k)$ and the x-axis at $X(h,0)$.

Now, it is given that A divides the line XY in ratio 1:2 internally.

$\therefore 3AX=2AY$

$A=\frac{3X+2Y}{5}$

$⟹(-2,6)=(\frac{3h+0}{5},\frac{0+2k}{5})$

$⟹(-2,6)=(\frac{3h}{5},\frac{2k}{5})$

$⟹-2=\frac{3h}{5},6=\frac{2k}{5}$

$h=-\frac{10}{3},k=15$

$\therefore$ equation of straight line $XY$ is

$\frac{y-15}{x-0}=\frac{0-15}{-\frac{10}{3}-0}$

$⟹\frac{y-15}{x}=\frac{9}{2}$

$9x-2y+30=0$

Hence the required equation of line is $9x-2y+30=0$

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