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

Front

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

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on its circumference.

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is half of the diameter, so if the diameter is 12, the radius is 6.

Front

How do you convert the diameter of a circle to its radius?

Back

To convert the diameter to radius, divide the diameter by 2.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

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

Back

In the equation (x - h)² + (y - k)² = r², the radius is the square root of r².

Front

What are the coordinates of the center of the circle given by the equation (x + 3)² + (y - 4)² = 16?

Back

The center is (-3, 4).

Front

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

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

How do you find the equation of a circle given its center and radius?

Back

Use the formula (x - h)² + (y - k)² = r², substituting the center (h, k) and radius r.