Equations of Circles Formula

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 does the center of a circle represent in its equation?

Back

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

Front

In the equation (x+2)² + (y+3)² = 49, what is the radius?

Back

The radius is 7, since √49 = 7.

Front

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

Back

The center is (4, -4).

Front

What is the significance of the number on the right side of the circle's equation?

Back

The number on the right side of the equation represents the square of the radius.

Front

How can you determine the center of the circle from the equation (x-3)² + (y-2)² = 16?

Back

The center is found at (3, 2), which are the values of h and k in the equation.

Front

What is the radius of the circle in the equation (x-3)² + (y+4)² = 121?

Back

The radius is 11, since √121 = 11.

Front

If the equation of a circle is given as (x+1)² + (y-5)² = 36, what is the center?

Back

The center is (-1, 5).

Front

What does the equation (x-2)² + (y+3)² = 9 represent graphically?

Back

It represents a circle with center (2, -3) and radius 3.