Find the equations of all lines having slope 2 and that are tangent to the curve `y=1/(x-3),\ \ x!=3` .

Explanation

Let `(x_{1}, y_{1})` be the point where the tangent is drawn to this curve.

Since, the point lies on the curve.

Hence,`y_{1}=frac{1}{x_{1}-3}`

` text { Now, } y =frac{1}{x-3} `
`Rightarrow frac{d y}{d x} =frac{-1}{(x-3)^{2}} `

Slope of tangent `=(frac{d y}{d x})=frac{-1}{(x_{1}-3)^{2}}`

Given that

Slope of the tangent `=2`


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