Equations of Circles

Front

What is the standard 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 variable 'r' represent in the equation of a circle?

Back

The radius of the circle.

Front

If the center of a circle is at (3, -4) and the radius is 5, what is the equation of the circle?

Back

(x - 3)² + (y + 4)² = 25.

Front

What is the diameter of a circle?

Back

The diameter is twice the radius.

Front

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

Back

The radius is the square root of the constant on the right side of the equation.

Front

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

Back

The center is (-2, 3).

Front

What is the radius of the circle given by the equation (x - 1)² + (y + 2)² = 36?

Back

The radius is 6.

Front

What is the relationship between the radius and the diameter?

Back

Diameter = 2 * Radius.

Front

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

Back

x² + y² = 16.

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.