Equations of Circles

Front

What is the standard equation of a circle?

Back

The standard 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 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 the form (x - h)² + (y - k)² = r².

Front

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

Back

The center of a circle is represented by the coordinates (h, k) in the standard equation (x - h)² + (y - k)² = r².

Front

If the equation of a circle is (x + 1)² + (y - 2)² = 9, what is the radius?

Back

The radius is 3, since √9 = 3.

Front

What is the diameter of a circle?

Back

The diameter is twice the radius of the circle.

Front

In the equation (x - 5)² + (y + 2)² = 16, what is the center of the circle?

Back

The center of the circle is (5, -2).

Front

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

Back

The diameter can be found by multiplying the radius by 2.

Front

What is the radius of the circle in the equation (x - 3)² + (y - 4)² = 4?

Back

The radius is 2, since √4 = 2.

Front

If the equation of a circle is (x + 2)² + (y - 3)² = 25, what is the diameter?

Back

The diameter is 10, since the radius is √25 = 5 and diameter = 2 * radius.

Front

What does the term (h, k) represent in the circle's equation?

Back

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