Point R (h, k) divides a line segment between the axes m the ratio `1: 2`. Find equation of the line.

Explanation

Let the equation of the line is,
`(x)/(a)+(y)/(b)=1`..........`(1)`
This line intersects `x`-axis at point `A(a,0)` and `y`-axis at point `B(0,b)`.
The coordinates of point `P` dividing the line segment `AB` in the ratio `1 : 2` are `(h,k)`.
`:. h=(1xx0+2xxa)/(1+2)impliesa=(3h)/(2)`
and `k=(1xxb+2xx0)/(1+2)impliesb=3k`
`:.` From equation `(1)`,
`(x)/(3h//2)+(y)/(3k)=1implies(2x)/(3h)+(y)/(3k)=1`
`implies 2kx+hy=3hk`