Question

A circle centered at the origin has a radius of 1/2 .

What is the equation of the circle?

Answer 1

(x-0)^2+(y-0)^2=(1/2)^2
4x^2+4y^2=1

Answer 2

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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