Circle Equations and Properties

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 and radius of a circle from its equation?

Back

To find the center and radius from the equation in standard form (x - h)² + (y - k)² = r², the center is (h, k) and the radius is r.

Front

What is the diameter of a circle?

Back

The diameter of a circle is the distance across the circle through its center, equal to twice the radius.

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is half of the diameter, so the radius is 6.

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 general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What does the term (x - h)² represent in the circle equation?

Back

The term (x - h)² represents the horizontal distance from the center of the circle to any point on the circle.

Front

What does the term (y - k)² represent in the circle equation?

Back

The term (y - k)² represents the vertical distance from the center of the circle to any point on the circle.

Front

What is the center of the circle given by the equation (x + 3)² + (y - 6)² = 25?

Back

The center is (-3, 6).

Front

What is the radius of the circle given by the equation (x - 4)² + (y - 2)² = 25?

Back

The radius is 5, since r² = 25.