Answer:
The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]
Step-by-step explanation:
Equation of a circle:
The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Centered at the the origin
Center (0,0), which means that [tex]x_0 = 0, y_0 = 0[/tex]
radius of 1/2
This means that [tex]r = \frac{1}{2}[/tex]
Equation:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 0)^2 + (y - 0)^2 = (\frac{1}{2})^2[/tex]
[tex]x^2 + y^2 = \frac{1}{4}[/tex]
The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]
