Determine the expression for the flipped unit circle equation

To determine the equation for a unit circle flipped over the y-axis, we start with the standard unit circle equation:

$x^2 + y^2 = 1$

When we flip the unit circle over the y-axis, we change the sign of the x-coordinate. Therefore, the new equation becomes:

$(-x)^2 + y^2 = 1$

Simplifying this, we get:

$x^2 + y^2 = 1$

Thus, the equation of the unit circle flipped over the y-axis is the same as the original unit circle.

Starting with the unit circle equation:

$x^2 + y^2 = 1$

Flipping the unit circle over the y-axis involves changing the sign of the x-coordinate, resulting in:

$(-x)^2 + y^2 = 1$

Since $(-x)^2$ is the same as $x^2$, we simplify to get:

$x^2 + y^2 = 1$

Thus, the flipped unit circle over the y-axis retains the equation:

$x^2 + y^2 = 1$

The unit circle equation is:

$x^2 + y^2 = 1$

When flipped over the y-axis:

$(-x)^2 + y^2 = 1$

Simplifying:

$x^2 + y^2 = 1$

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