Equation of a Circle

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 of a circle from its equation?

Back

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

Front

What is the circumference of a circle?

Back

The distance around a circle, calculated as C = 2πr, where r is the radius.

Front

What is the area of a circle?

Back

The space enclosed by a circle, calculated as A = πr², where r is the radius.

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 to rewrite the equation in standard form.

Front

What is the significance of the radius in the equation of a circle?

Back

The radius determines the size of the circle and is the distance from the center to any point on the circle.

Front

What is the center of the circle represented by the equation (x - 3)² + (y + 4)² = 25?

Back

The center is (3, -4).

Front

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

Back

The radius is 6 units.

Front

What is the relationship between the diameter and radius of a circle?

Back

The diameter is twice the radius (D = 2r).