The equation of straight line which passes through the point (-4,3) such that the portion of the line between the axes is divided by the point in ratio 5:3 is -

Options

A. 9x-20y+96=0
B. 9x+20y=24
C. 20x+9y+53=0
D. none of these

Answer

A

Explanation

Let the line cuts the axes at point A(a,0) and B(0,B). Now, given that (-4,3) divides AB in the ratio 5:3. Then,,-4=3a/8 and 3=5b/8. Therefore, a = -32/3 and b=24/5. Then using the intercept form x/a+y/b=1, the equation of line is
`-(3x)/(32) + (5y)/(24) = 1`
or 9x-20y+96 = 0