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

What does the center of a circle represent in its equation?

Back

The center of a circle is the point (h, k) in the equation (x-h)² + (y-k)² = r², which is equidistant from all points on the circle.

Front

How do you find the radius from the equation of a circle?

Back

The radius can be found by taking the square root of the value on the right side of the equation in standard form: (x-h)² + (y-k)² = r².

Front

What is the center of the circle with equation x² + y² = 25?

Back

The center is (0, 0).

Front

What is the radius of the circle with equation (x-2)² + (y+3)² = 16?

Back

The radius is 4.

Front

If the equation of a circle is (x+1)² + (y-2)² = 9, what is the center?

Back

The center is (-1, 2).

Front

What is the equation of a circle with center (3, -4) and radius 5?

Back

The equation is (x-3)² + (y+4)² = 25.

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 significance of the radius in the equation of a circle?

Back

The radius determines the size of the circle; it is the distance from the center to any point on the circle.

Front

What is the center of the circle defined by the equation (x-5)² + (y+7)² = 8?

Back

The center is (5, -7).