For each point, determine whether it lies on a circle centered at \((5,\text-6)\) with a radius of \(\sqrt{10}\). Explain how you know.

1. \((6,\text-3)\)
2. \((2,\text-6)\)

A circle has a center at \((2,2)\). What is the radius of the circle if:

1. \((\text-1,4)\) lies on the circle?
2. \((3,7)\) lies on the circle?

Find the distance between these points: \((\text-3,1)\) and \((4,\text-6)\).

Plot as many points as you can that lie a distance of 5 away from the point \((1,4)\).

For each point, determine whether it lies on a circle centered at \((\text-7,7)\) with a radius of \(\sqrt{13}\). Explain how you know.

1. \((\text-5,4)\)
2. \((\text-4,7)\)

A circle has a center at \((3,4)\). What is the radius of the circle if:

1. \((\text-2, \text-1)\) lies on the circle?
2. \((4, \text-5)\) lies on the circle?