Equation of a Circle part 1

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.

The center of a circle can be found from the equation (x - h)² + (y - k)² = r² by identifying the values of h and k.

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

The diameter of a circle is twice the radius, or d = 2r.

The center is (1, -4).

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

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

Completing the square involves rewriting a quadratic expression in the form (x - h)² to identify the center and radius of the circle.

The center is (2, -3) and the radius is 7.

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