Equations of Circles

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 standard form (x - h)² + (y - k)² = r² is given by the coordinates (h, k).

Front

What is the radius of a circle from its equation?

Back

The radius of a circle in the standard form (x - h)² + (y - k)² = r² is the square root of r².

Front

Convert the equation x² + y² - 4x + 6y - 12 = 0 to standard form.

Back

(x - 2)² + (y + 3)² = 25.

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius.

Front

If the center of a circle is at (0, 0) and the radius is 5, what is the equation of the circle?

Back

x² + y² = 25.

Front

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

Back

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

Front

Write the equation of a circle with center (3, -2) and radius 4.

Back

(x - 3)² + (y + 2)² = 16.

Front

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

Back

To determine the radius, take the square root of the value on the right side of the equation in standard form.