Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are `1` and `-6` , respectively.

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`

It is given that `a+b=1\ldots(i)` and `ab=-6\ldots(ii)`

From `(ii)`,

`b=\frac{-6}{a}`

Substitute `b=\frac{-6}{a}` in `(i)`, we get

`a-\frac{6}{a}=1`

`\implies a^2-a-6=0`

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