Equations of a circle

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 diameter of a circle from its equation?

Back

The diameter is twice the radius. If the equation is in standard form (x - h)² + (y - k)² = r², then the diameter is 2r.

Front

What are the coordinates of the center of a circle given by the equation (x - 4)² + (y - 3)² = 25?

Back

The center of the circle is at the point (4, 3).

Front

What is the radius of a circle with the equation (x + 2)² + (y - 1)² = 36?

Back

The radius is 6 units, since r² = 36, so r = √36 = 6.

Front

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

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What is the radius of a circle with the equation (x - 7)² + y² = 9?

Back

The radius is 3 units, since r² = 9, so r = √9 = 3.

Front

What does the equation (x + 1)² + (y - 3)² = 9 represent?

Back

This represents a circle with center (-1, 3) and radius 3 units.

Front

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

Back

The equation is x² + y² = 25.

Front

What is the relationship between the radius and diameter of a circle?

Back

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

Front

How can you determine the center and radius from the equation (x - 2)² + (y + 4)² = 16?

Back

The center is (2, -4) and the radius is 4 units, since r² = 16.