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 radius from the equation of a circle?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form: (x - h)² + (y - k)² = r².

Front

What is the center of the circle in the equation (x - 5)² + (y + 3)² = 16?

Back

The center of the circle is (5, -3).

Front

In the equation (x + 2)² + (y - 1)² = 9, what is the radius?

Back

The radius is 3, since √9 = 3.

Front

What does the equation (x - 1)² + (y - 4)² = 25 represent?

Back

This represents a circle with center (1, 4) and radius 5, since √25 = 5.

Front

If the equation of a circle is (x + 3)² + (y - 2)² = 36, what is the radius?

Back

The radius is 6, since √36 = 6.

Front

What is the equation of a circle with center (0, 0) and radius 4?

Back

The equation is x² + y² = 16.

Front

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

Back

The center can be determined from the equation (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center.

Front

What is the radius of the circle given by the equation (x - 2)² + (y + 5)² = 49?

Back

The radius is 7, since √49 = 7.

Front

In the equation (x + 1)² + (y - 3)² = 1, what is the center?

Back

The center is (-1, 3).