Graphing Circles

Front

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

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

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

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

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

Back

The radius is √25 = 5.

Front

What does the term 'h' represent in the circle equation?

Back

The 'h' value represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the circle equation?

Back

The 'k' value represents the y-coordinate of the center of the circle.

Front

If the equation of a circle is x² + y² = 36, what is the radius?

Back

The radius is √36 = 6.

Front

What is the center of the circle given by the equation (x + 1)² + (y - 4)² = 9?

Back

The center is (-1, 4).

Front

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

Back

Complete the square for both x and y terms.

Front

What is the equation of a circle with center (0, 0) and radius 3?

Back

x² + y² = 9.

Front

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

Back

The center is (5, -2).