The circle with center at the origin and radius r has equation x^2 + y^2 = r^2. True or false?

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

Multiple Choice

The circle with center at the origin and radius r has equation x^2 + y^2 = r^2. True or false?

The distance from the origin to any point (x, y) is sqrt(x^2 + y^2). If that distance equals r, squaring both sides gives x^2 + y^2 = r^2. This equation captures exactly all points that lie at distance r from the origin, which is what a circle of radius r centered at the origin is. So the statement is true. Note that r is nonnegative by definition of a radius; if someone used a negative r, the equation would still describe the same circle as using |r|. For example, r = 0 gives just the origin, and r = 3 gives the circle of radius 3.

The distance from the origin to any point (x, y) is sqrt(x^2 + y^2). If that distance equals r, squaring both sides gives x^2 + y^2 = r^2. This equation captures exactly all points that lie at distance r from the origin, which is what a circle of radius r centered at the origin is. So the statement is true. Note that r is nonnegative by definition of a radius; if someone used a negative r, the equation would still describe the same circle as using |r|. For example, r = 0 gives just the origin, and r = 3 gives the circle of radius 3.

More practice questions