The equation of the circle centered at the origin has a radius of \(\dfrac{1}{2}\) is \(x^2+y^2 = \dfrac{1}{4}\).
General Equation of a Circle
\((x-h)^2+(y-k)^2 = R^2\)
where,
(h, k) is the coordinates of the center of the circle,
r is the radius of the circle.
Given to us
Centered at the origin
Radius of 1/2
To find
As the circle is centered at the origin, the coordinates will be (0,0). for the center while the radius is already given as \(\dfrac{1}{2}\).
Substituting the values in the general equation of the circle,
\((x-h)^2+(y-k)^2 = R^2\)
\((x-0)^2+(y-0)^2 = (\dfrac{1}{2})^2\)
\(x^2+y^2 = \dfrac{1}{4}\)
Hence, the equation of the circle centered at the origin has a radius of \(\dfrac{1}{2}\) is \(x^2+y^2 = \dfrac{1}{4}\).
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