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Find the equations of all lines having s...

Find the equations of all lines having slope 0 which are tangent to the curve `y=1/(x^2-2x+3)`.

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The equation of the given curve is `y=1/(x^2-2x+3`
The slope of the tangent to the given curve at any point (x,y) is given by,
`dy/dx=-(2x-2)/((x^2-2x+3)^3)=-(2(x-1))/((x^2-2x+3)^3)`
If the slope of the tangent is 0, then we have:
`-(2(x-1))/((x^2-2x+3)^3)=0`
When `x=1` , `y=1/2`
the equation of the tangent through `(1,1/2)` is given by
`y-1/2=0(x-1)impliesy=1/2`
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