Find the points on the curve `x^2+y^2-2x-3=0` at which the tangents are parallel to the x-axis and y-axis.

Answer

Points at which the tangents are parallel to the `x`-axis are
`(1,2)` and `(1,-2)`.

Explanation

The equation of the given curve is `x^{2}+y^{2}-2 x-3=0`.

On differentiating with respect to `x`, we have:
$$
\begin{aligned}
&2 x+2 y \frac{d y}{d x}-2=0 \\
&\Rightarrow y \frac{d y}{d x}=1-x \\
&\Rightarrow \frac{d y}{d x}=\frac{1-x}{y}
\end{aligned}
...