### Home > CCG > Chapter 12 > Lesson 12.1.3 > Problem12-45

12-45.

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

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.

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

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.

$x = −2$ or $2$

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

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