Equation of a Circle

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 represents the distance from the center to any point on the circle, and it is the square root of the value on the right side of the equation in standard form.

Front

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

Back

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

Front

What is the center of the circle in the equation (x + 1)² + (y - 5)² = 9?

Back

The center is (-1, 5).

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

Back

The equation is x² + y² = 9.

Front

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

Back

The center is (4, -2).

Front

What is the radius of the circle given by the equation (x + 3)² + (y - 1)² = 36?

Back

The radius is 6, since r² = 36, and r = √36 = 6.

Front

If the center of a circle is (2, -3) and the radius is 7, what is the equation of the circle?

Back

The equation is (x - 2)² + (y + 3)² = 49.