Question

This circle is centered at the origin, and the length of its radius is 2 what is the circles equation?

Answer 1

x^2 + y^2 = r^2 so here it is:

x^2 + y^2 = 4

Option D

Answer 2

Option D is correct

`x^2+y^2=4`

Explanation:

The general equation of circle with center (h, k) and radius r is given by:

`(x-h)^2+(y-k)^2=r^2` ....[1]

As per the statement:

This circle is centered at the origin, and the length of its radius is 2.

Center = (h, k)=(0, 0)

radius(r) = 2 units

Substitute the given values in [1] we have;

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

⇒
`x^2+y^2=4`

Therefore, the equation of circle is,
`x^2+y^2=4`