Equations of Circles

Front

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

Back

The standard form of the equation of a circle 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 of a circle is the distance from the center to any point on the circle, represented by r in the equation (x - h)² + (y - k)² = r².

Front

If the equation of a circle is (x + 3)² + (y - 2)² = 16, what is the radius?

Back

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

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius, d = 2r.

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 is the center of the circle with the equation (x - 1)² + (y + 5)² = 36?

Back

The center is (1, -5).

Front

What is the radius of the circle represented by the equation (x - 2)² + (y + 3)² = 49?

Back

The radius is 7 units, since r² = 49, thus r = √49 = 7.

Front

In the equation (x + 4)² + (y - 1)² = 25, what is the diameter?

Back

The diameter is 10 units, since the radius is 5 units.

Front

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

Back

The equation is x² + y² = 25.