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

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

Back

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

Front

What is the radius of a circle in the equation (x - 4)² + (y + 1)² = 25?

Back

The radius is 5, since r² = 25, thus r = √25 = 5.

Front

If the diameter of a circle is 10, what is the radius?

Back

The radius is 5, since the radius is half of the diameter.

Front

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

Back

The equation is x² + y² = 16.

Front

In the equation (x + 1)² + (y - 3)² = 36, what is the center of the circle?

Back

The center is (-1, 3).

Front

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

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

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

Back

To convert, complete the square for the x and y terms in the equation Ax² + Ay² + Bx + Cy + D = 0.

Front

What is the significance of the number on the right side of the equation (x - 2)² + (y + 3)² = 49?

Back

The number 49 represents the square of the radius, so the radius is √49 = 7.

Front

What is the center of the circle in the equation (x - 5)² + (y + 2)² = 9?

Back

The center is (5, -2).