{
  "problem": "The equation of a circle $C$ is $x^2+y^2+12x+6y+29 = 0$. What is its center $(h, k)$ and its radius $r$ ?",
  "hints": [
    "To find the equation in standard form, complete the square.",
    "$(x^2+12x) + (y^2+6y) = -29$",
    "$(x^2+12x+36) + (y^2+6y+9) = -29 + 36 + 9$",
    "$(x+6)^{2} + (y+3)^{2} = 16 = 4^2$",
    "Thus, $(h, k) = (-6, -3)$ and $r = 4$."
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/490/1608221380.json'}