The equation of a semicircle that is the upper half of the circle centered at the origin with radius 2 is $y=\sqrt{4-x^{2}}$ .

Question

The equation of a semicircle that is the upper half of the circle centered at the origin with radius 2 is $y=\sqrt{4-x^{2}}$.

Quizplus · Accepted Answer

The equation of a circle centered at the origin with radius $r$ is $x^2 + y^2 = r^2$. For a circle with radius 2, this becomes $x^2 + y^2 = 4$. Solving for $y$ to get the upper semicircle, we take the positive square root, resulting in $y = \sqrt{4 - x^2}$.

The Equation of a Semicircle That Is the Upper Half y=4−x2y=\sqrt{4-x^{2}}y=4−x2​

The Equation of a Semicircle That Is the Upper Half $y=\sqrt{4-x^{2}}$