{
  "problem": "The equation of hyperbola $H$ is $\\dfrac {(x-8)^{2}}{64}-\\dfrac {(y+3)^{2}}{9} = 1$. What are the asymptotes?",
  "hints": [
    "We want to rewrite the equation in terms of",
    "$y$",
    ", so start off by moving the",
    "$y$",
    "terms to one side:",
    "$\\dfrac {(y+3)^{2}}{9} = - 1 + \\dfrac {(x-8)^{2}}{64}$",
    "Multiply both sides of the equation by",
    "$9$",
    "$(y+3)^{2} = { - 9 + \\dfrac{ (x-8)^{2} \\cdot 9 }{64}}$",
    "Take the square root of both sides.",
    "$\\sqrt{(y+3)^{2}} = \\pm \\sqrt { - 9 + \\dfrac{ (x-8)^{2} \\cdot 9 }{64}}$",
    "$ y + 3 = \\pm \\sqrt { - 9 + \\dfrac{ (x-8)^{2} \\cdot 9 }{64}}$",
    "As",
    "$x$",
    "approaches positive or negative infinity, the constant term in the square root matters less and less, so we can just ignore it.",
    "$y + 3 \\approx \\pm \\sqrt {\\dfrac{ (x-8)^{2} \\cdot 9 }{64}}$",
    "$y + 3 \\approx \\pm \\left(\\dfrac{3 \\cdot (x - 8)}{8}\\right)$",
    "Subtract $3$ from both sides and rewrite as an equality in terms of $y$ to get the equation of the asymptotes: $y = \\pm \\dfrac{3}{8}(x - 8) -3$"
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/402/1608223255.json'}