Find the points of intersection of the line y=2x+1 and the circle `x^2+y^2-2y=0`. Find the equation of the tangent to the circle at one of the point of intersection.

Explanation

To find the points of intersection of the line \( y = 2x + 1 \) and the circle \( x^2 + y^2 - 2y = 0 \), and then derive the equation of the tangent to the circle at one of the intersection points, we can follow these steps:

### Step 1: Rewrite the Circle's Equation
The equation of the circle is given as:
\[ x^2 + y^2 - 2y = 0 \]
We can rewrite this as:
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