a. The general equation for a circle centered at with radius is
The described circle has equation
We know the circle passes through the origin. This means that the equation above holds for and . The distance between any point on the circle and its center is the radius, so we can use this fact to determine :
So the circle's equation is
b. If the distance between point B and the center is less than , then B lies inside the circle. If the distance is greater than , it falls outside the circle. Otherwise, if the distance is exactly , then B lies on the circle.
The distance from B to the center is
, so , which means B falls outside the circle.