Find the coordinates of the point where the line $ y = 1 $ intersects the unit circle

To find the coordinates where the line $ y = 1 $ intersects the unit circle, we start by recalling the equation of the unit circle:

$ x^2 + y^2 = 1 $

Substituting $ y = 1 $ into the unit circle equation, we get:

$ x^2 + 1^2 = 1 $

Simplifying,

$ x^2 + 1 = 1 $

$ x^2 = 0 $

$ x = 0 $

Therefore, the point of intersection is:

$ (0, 1) $

Start with the equation of the unit circle:

$ x^2 + y^2 = 1 $

Substitute $ y = 1 $:

$ x^2 + 1 = 1 $

Solve for $ x $:

$ x^2 = 0 $

Thus,

$ x = 0 $

The coordinates are:

$ (0, 1) $

Substitute $ y = 1 $ in the unit circle equation:

$ x^2 + 1 = 1 $

Solve:

$ x = 0 $

Coordinates:

$ (0, 1) $

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