The equation of the straight line which passes through the point `(-4,3)` such that the portion of the line between the axes is divided internally be the point in the ratio `5:3` is (a) `9x-20 y+96=0` (b) `9x+20 y=24` (c) `20 x-9y+53=0` (d) none of these

Answer

N/a

Explanation

Since, the line intersects X and Y -axes respectively at A(x,0)and B (0,y).

`4=(5xx0+3x)/(5+3)`
`rArr -4=(3x)/(8)rArrx=(-32)/(3)`
and `3=(5.y+3.0)/(5+3)`
`rArr 3=(5y)/(8)rArry=(24)/(5)`
Since, the intercept on the Xand Y-axes respectively are a `=(-32)/(3)` and `b=(24)/(5)`
`therefore` Equation of required line is `(x)/(-32//3)+(y)/(24//5)=1`
`rArr (-3x)/(32)+(5y)/(24)=1`
`rArr -9x+20y=96`
`rArr 9x-20y+96=0`