Consider the circle that is centered at the origin and contains the point $(0,3)$.

1. Use geometry and the definition of a circle, but not the algebraic equation for a circle, to prove or disprove that the point $(1,\ \sqrt{5})$ lies on this circle.

   Hint (a):

   Any line from the origin to the edge of the circle will be 3 units long.

   More Help (a):

   Find the distance from the origin to $(1,\ \sqrt{5})$.

2. Find at least one value of x so that the point $(x, \sqrt { 5 })$ lies on the circle.

   Answer (b):

   $x = −2$ or $2$

3. Name $3$ other points on this same circle.

   Hint (c):

   Write the equation for this circle and find values of $x$ and $y$ that satisfy the equation.