Question

A circle centered ar the the orgin has a radius of 1/2 what is the equation of the circle

Answer 1

The equation of the circle is
`x^2 + y^2 = (1)/(4)`

Explanation:

Equation of a circle:

The equation of a circle with center
`(x_0,y_0)` and radius r is given by:

`(x - x_0)^2 + (y - y_0)^2 = r^2`

Centered at the the origin

Center (0,0), which means that
`x_0 = 0, y_0 = 0`

radius of 1/2

This means that
`r = (1)/(2)`

Equation:

`(x - x_0)^2 + (y - y_0)^2 = r^2`

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

`x^2 + y^2 = (1)/(4)`

The equation of the circle is
`x^2 + y^2 = (1)/(4)`