Find eqn of lines pass through origin and trisect the intercept of line` 3x +4y =12` between the axes. `4`.

Explanation

Let the intersecting point of the given line and the required line be `(h,k)`

Equation of line in intercept form is `\frac{x}{a}+\frac{y}{b}=1`, where its x- intercept is `a` and y- intercept is `b`

Given line equation is `3x+4y=12`

`\implies \frac{x}{4}+\frac{y}{3}=1`

`\implies a=4` and `b=3`

`\implies A(4,0)` and `B(0,3)` is on the given line.

And it is given the point `(h,k)` divides the line segment `A(4,0)` and `B(0,3)` in the ratio `1:2`.

By section formula,

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