Circle Equations

Front

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

Back

The standard form of a circle's equation 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 standard form (x - h)² + (y - k)² = r² is given by the point (h, k).

Front

What is the radius of a circle in the equation (x - 4)² + (y + 1)² = 9?

Back

The radius is 3, since r² = 9, thus r = √9 = 3.

Front

Convert the equation x² + y² - 6x - 8y + 9 = 0 to standard form.

Back

(x - 3)² + (y - 4)² = 4.

Front

What is the radius of the circle given by the equation (x + 2)² + (y - 5)² = 16?

Back

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

Front

Identify the center of the circle from the equation (x - 1)² + (y + 2)² = 25.

Back

The center is (1, -2).

Front

What does the term 'h' represent in the standard form of a circle's equation?

Back

In the standard form (x - h)² + (y - k)² = r², 'h' represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the standard form of a circle's equation?

Back

In the standard form (x - h)² + (y - k)² = r², 'k' represents the y-coordinate of the center of the circle.

Front

How do you determine the radius from the equation of a circle?

Back

The radius can be determined by taking the square root of the value 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 x² + y² - 4x - 6y + 9 = 0?

Back

The center is (2, 3).