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At what point on the circle x^2+y^2-2x-4...

At what point on the circle `x^2+y^2-2x-4y+1=0,` the tangent is parallel to x-axis.

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The equation of the circle is,`x^{2}+y^{2}-2 x-4 y+1=0...(i)`.
At points where the tangent is parallel to x-axis the slope is `0` .
Differentiate the above equation with respect to x.
Thus,
`2x+2yy^{prime}-2-4y^{prime}=0`
`Rightarrow y^{prime}(y-2)=1-x`
...
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