Graphing Circles

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

The center of a circle in the standard form (x - h)² + (y - k)² = r² is (h, k).

Front

What is the radius of a circle given the equation (x - 2)² + (y + 3)² = 25?

Back

The radius is √25 = 5.

Front

If the diameter of a circle is 10, what is the radius?

Back

The radius is half of the diameter, so the radius is 10 / 2 = 5.

Front

What is the equation of a circle with center (0, 0) and radius 3?

Back

The equation is x² + y² = 9.

Front

How do you convert the equation (x + 1)² + (y - 2)² = 16 into standard form?

Back

The equation is already in standard form with center (-1, 2) and radius 4.

Front

What is the center of the circle given by the equation (x - 4)² + (y + 1)² = 36?

Back

The center is (4, -1).

Front

What does the term 'radius' refer to in a circle?

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

How do you determine the radius from the equation (x + 2)² + (y - 5)² = 49?

Back

The radius is √49 = 7.

Front

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

Back

The diameter is twice the radius (Diameter = 2 * Radius).