QuestionFind the equation of a circle with center at the origin and radius $\frac{1}{2}$ . Options: A. $x^{2}+y^{2}=\frac{1}{4}$ B. $x^{2}+y^{2}=\frac{1}{2}$ C. $x^{2}+y^{2}=1$ D. $x^{2}+y^{2}=2$

Studdy Solution

STEP 1

Assumptions1. The circle is centered at the origin (0,0) . The radius of the circle is $\frac{1}{}$

STEP 2

The general equation for a circle centered at the origin is given by $x^{2}+y^{2}=r^{2}$ where $r$ is the radius of the circle.

STEP 3

Substitute the given radius into the equation of the circle.
$x^{2}+y^{2}=\left(\frac{1}{2}\right)^{2}$

STEP 4

Calculate the square of the radius.
$x^{2}+y^{2}=\frac{1}{4}$ So, the equation of the circle is $x^{2}+y^{2}=\frac{1}{4}$ . Therefore, the correct answer is option A.

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