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 does the radius of a circle represent in its equation?

Back

The radius of a circle represents the distance from the center to any point on the circle, and it is the square root of the value on the right side of the equation in standard form.

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 both x and y terms.

Front

What is the radius of the circle given by the equation (x - 3)² + (y + 4)² = 16?

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

What is the center of the circle represented by the equation (x + 1)² + (y - 5)² = 25?

Back

The center is (-1, 5).

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 significance of the number on the right side of the circle's equation in standard form?

Back

The number on the right side of the equation (r²) indicates the square of the radius of the circle.

Front

How do you determine the radius from the equation (x + 2)² + (y - 3)² = 49?

Back

The radius is 7, since r² = 49, thus r = √49 = 7.

Front

What is the center of the circle given by the equation (x - 4)² + (y + 2)² = 36?

Back

The center is (4, -2).