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, identify the equation in the form (x - h)² + (y - k)² = r². The radius is the square root of the number on the right side of the equation.

Front

What is the center of a circle in the equation (x - 3)² + (y + 2)² = 16?

Back

The center of the circle is (3, -2).

Front

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

Back

The equation is x² + y² = 25.

Front

What is the diameter of a circle if the radius is 6?

Back

The diameter is 12, calculated as Diameter = 2 * Radius.

Front

What are the coordinates of the center and radius of the circle (x + 1)² + (y - 4)² = 36?

Back

Center: (-1, 4), Radius: 6 units.

Front

Write the equation of a circle with center (2, -3) and radius 4.

Back

The equation is (x - 2)² + (y + 3)² = 16.

Front

What is the radius of the circle represented by the equation (x - 5)² + (y + 1)² = 49?

Back

The radius is 7, since r² = 49.

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.

Front

What is the equation of a circle with center (0, 0) and radius 10?

Back

The equation is x² + y² = 100.