Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Explanation

An equation in intercept form is `\frac{x}{a}+\frac{y}{b}=1` where x- intercept is `a` and y- intercept is `b`

It is given `a+b=9`

`\implies b=9-a`

Thus, the required equation becomes `\frac{x}{a}+\frac{y}{9-a}=1` which passes through `(2,2).`

So, `(2,2)` will satisfy the equation.

Therefore, `\frac{2}{a}+\frac{2}{9-a}=1`

`\implies \frac{18}{9a-a^2}=1`

`\implies a^2-9a+18=0`

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