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 radius of a circle from its equation?

Back

To find the radius from the equation (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the relationship between diameter and radius?

Back

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

Front

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

Back

The equation is x² + y² = 25.

Front

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

Back

The center of a circle is the point that is equidistant from all points on the circle.

Front

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

Back

From the equation (x - h)² + (y - k)² = r², the center is (h, k).

Front

What is the diameter of a circle with a radius of 3?

Back

The diameter is 6, since d = 2r.

Front

In the equation (x + 1)² + (y - 4)² = 16, what is the center of the circle?

Back

The center is (-1, 4).

Front

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

Back

The radius is 5, since r² = 25.

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 general form Ax² + Ay² + Bx + Cy + D = 0.