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

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

Back

The variable 'r' represents the radius of the circle.

Front

How do you find the radius from the equation (x + 3)² + (y - 1)² = 49?

Back

The radius is the square root of 49, which is 7.

Front

What is the center of the circle in the equation (x - 4)² + (y + 2)² = 36?

Back

The center of the circle is (4, -2).

Front

If the radius of a circle is 5, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 25.

Front

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

Back

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

Front

How do you convert the equation (x - 1)² + (y + 3)² = 16 into standard form?

Back

The equation is already in standard form, where the center is (1, -3) and the radius is 4.

Front

What is the diameter of a circle with the equation (x + 2)² + (y - 5)² = 64?

Back

The diameter is 16, since the radius is 8 (the square root of 64).

Front

In the equation of a circle, what does (h, k) represent?

Back

(h, k) represents the center of the circle.

Front

What is the radius of the circle given by the equation (x - 6)² + (y + 4)² = 81?

Back

The radius is 9, since the square root of 81 is 9.