Equations of Circles

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r²

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

x² + y² = 25

Front

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

Back

Center is (3, -4)

Front

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

Back

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

Front

What is the diameter of a circle if the radius is 4?

Back

Diameter = 2 * radius = 8

Front

Convert the general form of a circle equation x² + y² + 6x - 8y + 9 = 0 to standard form.

Back

(x + 3)² + (y - 4)² = 16

Front

What are the coordinates of the center and radius of the circle given by the equation (x + 2)² + (y - 1)² = 9?

Back

Center (-2, 1), Radius = 3

Front

Determine the center and radius of the circle represented by the equation x² + y² - 4x - 6y + 12 = 0.

Back

Center (2, 3), Radius = 2

Front

What is the radius of the circle given by the equation (x - 1)² + (y + 2)² = 25?

Back

Radius = 5

Front

Write the equation of a circle with center (-1, 2) and radius 4.

Back

(x + 1)² + (y - 2)² = 16