Find the equation of the line which passes through `P(1,-7)` and meets the axes at `Aa n dB` respectively so that `4A P-3B P=0.`

Explanation

Let the required equation in intercept form be `\frac{x}{a}+\frac{y}{b}=1`

Therefore, its x- intercept is `a` and y- intercept is `b`

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

And `4A P-3B P=0.`

`\implies \frac{AP}{BP}=\frac{3}{4}`

`\implies P(1,-7)` divides the line segment `A(a,0)` and `B(0,b)` in the ratio `3:4`.

By section formula,

`(1,-7)=(\frac{3\times0+4\timesa}{7},\frac{3\times b+4\times 0}{7})`

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