Find the equation of a line which passes through the point `(22,-6)` and is such that the intercept on x-axes exceeds the intercept on y-axis by 5.

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+5`

`\implies b=a-5`

Thus, the required equation becomes `\frac{x}{a}+\frac{y}{a-5}=1` which passes through `(22,-6).`

So, `(22,-6)` will satisfy the equation.

Therefore, `\frac{22}{a}+\frac{-6}{a-5}=1`

`\implies \frac{16a-110}{a^2-5a}=1`

`\implies a^2-21a+110=0`

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