Examining whether a circle goes through any of a given set of points

Question

In a rectangular coordinate system, the circle is created at the central and passes through point $P(0,-3)$. Which of the following points does it also pass through?

1. $(3,3)$
2. $(-2 \sqrt 2,-1)$
3. $(2,6)$
4. $(- \sqrt 3, \sqrt 3)$
5. $(-3,4)$

Answer 1

Hint:

If, indeed, "created at the central" means "centered at the origin" as you think, then we know the circle has center $(0,0)$. Since it goes through $(0,-3)$, we can conclude it has radius $3$. Accordingly, recall the general form for a circle in the plane:

$$(x-h)^2 + (y-k)^2 = r^2$$

where $(h,k)$ is the center, and $r$ the radius. With the knowledge $(h,k)=(0,0)$ and $r=3$ as described previously, create the equation for the circle, and then plug in each point you're given, seeing if each creates a true statement.