Circle Equations Flashcard

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation 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 radius from the equation of a circle?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form: (x - h)² + (y - k)² = r².

Front

What is the center of the circle in the equation (x - 1)² + (y + 3)² = 25?

Back

The center of the circle is (1, -3).

Front

If the radius of a circle is 5, what is the equation of the circle centered at (2, -1)?

Back

The equation of the circle is (x - 2)² + (y + 1)² = 25.

Front

What does the term 'diameter' refer to in a circle?

Back

The diameter is the distance across the circle through its center, equal to twice the radius.

Front

In the equation (x + 4)² + (y - 2)² = 36, what is the radius?

Back

The radius is 6, since √36 = 6.

Front

How do you determine the center of a circle from its equation?

Back

The center can be determined from the equation (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center.

Front

What is the relationship between the radius and diameter?

Back

The diameter is twice the radius: Diameter = 2 * Radius.

Front

What is the equation of a circle with center at (0, 0) and radius 4?

Back

The equation is x² + y² = 16.

Front

In the equation (x - 3)² + (y + 4)² = 121, what is the radius?

Back

The radius is 11, since √121 = 11.