Find the direction in which a straight line must be drawn through the point `(-1," "2)` so that its point of intersection with the line `x" "+" "y" "=" "4` may be at a distance of 3 units from this point.

Explanation

Let `y=mx+c` be a line passing through `(-1,2)`

`\implies 2=m(-1)+c`

`\implies c=m+2`

Let `x+y=4\ldots`(i)

and `y=mx+m+2ldots`(ii)

Putting equation (ii) in (i), we get `x+mx+m+2=4`

`\implies x=frac{2-m}{1+m}`

and `y=frac{5m+2}{1+m}`

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