Circles in standard form

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is given by the point (h, k).

Front

What does the radius of a circle represent in its equation?

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on its circumference.

Front

In the equation (x - 3)² + (y - 2)² = 16, what is the radius?

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

What is the relationship between the diameter and radius of a circle?

Back

The diameter is twice the radius. If r is the radius, then the diameter d = 2r.

Front

How do you convert the diameter of a circle to its radius?

Back

To convert the diameter to radius, divide the diameter by 2. r = d/2.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

If the center of a circle is at (-5, 2) and the radius is 6, what is the equation?

Back

The equation is (x + 5)² + (y - 2)² = 36.

Front

What does it mean if the radius of a circle is 0?

Back

If the radius is 0, the circle is reduced to a single point, which is the center.

Front

How can you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the point to the center. If the distance < r, it's inside; if = r, it's on; if > r, it's outside.