Equations of Circles

Front

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

Back

(x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

Front

What does the center of a circle represent in its equation?

Back

The center (h,k) represents the point around which the circle is drawn.

Front

How do you find the radius from the standard equation of a circle?

Back

The radius r is the square root of the constant on the right side of the equation (r = √constant).

Front

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

Back

The radius is 4, since r² = 16.

Front

What does the term (h,k) represent in the equation of a circle?

Back

(h,k) represents the coordinates of the center of the circle.

Front

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

Back

The center is (-2, 5).

Front

What is the radius of the circle given by the equation (x-1)² + (y+3)² = 49?

Back

The radius is 7, since r² = 49.

Front

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

Back

It represents the square of the radius (r²).

Front

In the equation x² + y² = 25, what is the center of the circle?

Back

The center is (0, 0).

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for both x and y terms.