randRange(-9, 9) randRange(-9, 9) randRange(1, 7) H === 0 ? "x^2" : expr(["^", ["+", "x", -H], 2]) K === 0 ? "y^2" : expr(["^", ["+", "y", -K], 2]) -2 * H -2 * K H * H + K * K - R * R

The equation of a circle C is expr(["+", "x^2", "y^2", D === 0 ? null : ["*", D, "x"], E === 0 ? null : ["*", E, "y"], F === 0 ? null : F ]) = 0.

What is its center (h, k) and its radius r?

(h, k) = (H, K)

r = {}R

To find the equation in standard form, complete the square.

(expr(["+", "x^2", ["*", D, "x"]])) + (expr(["+", "y^2", ["*", E, "y"]])) = -F

(expr(["+", "x^2", ["*", D, "x"], H * H])) + (expr(["+", "y^2", ["*", E, "y"], K * K])) = -F + H * H + K * K

X2T + Y2T = R * R = R^2

Thus, (h, k) = (H, K) and r = R.