Circle Equations

Front

What is the standard equation of a circle?

Back

The standard equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Front

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

Back

The center (h, k) in the equation (x - h)² + (y - k)² = r² represents the point around which the circle is drawn.

Front

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

Back

The radius r can be found by taking the square root of the constant on the right side of the equation (x - h)² + (y - k)² = r².

Front

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

Back

x² + y² = 25.

Front

If a circle has a center at (3, -2) and a radius of 4, what is its equation?

Back

(x - 3)² + (y + 2)² = 16.

Front

What is the equation of a circle with center (-1, 1) and radius 3?

Back

(x + 1)² + (y - 1)² = 9.

Front

How do you convert the general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

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

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

What is the equation of a circle with center (2, 3) and radius 2?

Back

(x - 2)² + (y - 3)² = 4.

Front

What does it mean if the radius of a circle is zero?

Back

If the radius is zero, the circle is reduced to a single point, which is the center.