[
  {
    "Question": "What is the standard form of the equation of a circle with center at (h, k) and radius r?",
    "Answer": "A",
    "Explanation": "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.",
    "PictureURL": "",
    "OptionA": "(x - h)² + (y - k)² = r²",
    "OptionB": "(x + h)² + (y + k)² = r²",
    "OptionC": "x² + y² = r²",
    "OptionD": "(x - h)² + (y + k)² = r²",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Equations of Circles",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "geometry/circles/equations"
  },
  {
    "Question": "What is the center of the circle given by the equation (x - 3)² + (y + 2)² = 16?",
    "Answer": "B",
    "Explanation": "The center of the circle can be found from the equation in standard form, which shows that the center is at (3, -2).",
    "PictureURL": "",
    "OptionA": "(3, 2)",
    "OptionB": "(3, -2)",
    "OptionC": "(-3, 2)",
    "OptionD": "(-3, -2)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Circle Center",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "geometry/circles/center"
  },
  {
    "Question": "What is the radius of the circle defined by the equation (x + 1)² + (y - 4)² = 25?",
    "Answer": "A",
    "Explanation": "The radius is the square root of the number on the right side of the equation. Here, √25 = 5.",
    "PictureURL": "",
    "OptionA": "5",
    "OptionB": "4",
    "OptionC": "6",
    "OptionD": "25",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Circle Radius",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "geometry/circles/radius"
  },
  {
    "Question": "Which of the following points lies on the circle given by (x - 1)² + (y - 2)² = 9?",
    "Answer": "C",
    "Explanation": "To determine if a point lies on the circle, substitute the point's coordinates into the equation. (4, 2) satisfies the equation.",
    "PictureURL": "",
    "OptionA": "(1, 2)",
    "OptionB": "(1, 5)",
    "OptionC": "(4, 2)",
    "OptionD": "(1, -1)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Points on a Circle",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "geometry/circles/points"
  },
  {
    "Question": "What is the equation of a circle with center at (0, 0) and radius 4?",
    "Answer": "A",
    "Explanation": "The standard form for a circle centered at the origin is x² + y² = r². Here, r = 4, so the equation is x² + y² = 16.",
    "PictureURL": "",
    "OptionA": "x² + y² = 16",
    "OptionB": "x² + y² = 4",
    "OptionC": "(x - 0)² + (y - 0)² = 4",
    "OptionD": "(x + 0)² + (y + 0)² = 16",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Circle Equation from Center and Radius",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "geometry/circles/equation_from_center_radius"
  },
  {
    "Question": "If a circle has the equation (x - 5)² + (y + 3)² = 36, what is the diameter of the circle?",
    "Answer": "B",
    "Explanation": "The diameter is twice the radius. Here, the radius is √36 = 6, so the diameter is 2 * 6 = 12.",
    "PictureURL": "",
    "OptionA": "6",
    "OptionB": "12",
    "OptionC": "18",
    "OptionD": "36",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Circle Diameter",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "geometry/circles/diameter"
  },
  {
    "Question": "What is the general form of the equation of a circle?",
    "Answer": "C",
    "Explanation": "The general form of a circle's equation is x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.",
    "PictureURL": "",
    "OptionA": "x² + y² = r²",
    "OptionB": "(x - h)² + (y - k)² = r²",
    "OptionC": "x² + y² + Dx + Ey + F = 0",
    "OptionD": "(x + h)² + (y + k)² = r²",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "General Form of Circle Equation",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "geometry/circles/general_form"
  },
  {
    "Question": "Which of the following equations represents a circle with center at (2, -3) and radius 5?",
    "Answer": "A",
    "Explanation": "Using the standard form, the equation is (x - 2)² + (y + 3)² = 25, which simplifies to the correct option.",
    "PictureURL": "",
    "OptionA": "(x - 2)² + (y + 3)² = 25",
    "OptionB": "(x + 2)² + (y - 3)² = 25",
    "OptionC": "(x - 2)² + (y - 3)² = 5",
    "OptionD": "(x + 2)² + (y + 3)² = 25",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Circle Equation from Center and Radius",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "geometry/circles/equation_center_radius"
  },
  {
    "Question": "What is the distance from the center of the circle (1, 1) to the point (4, 5)?",
    "Answer": "C",
    "Explanation": "Using the distance formula, the distance is √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.",
    "PictureURL": "",
    "OptionA": "4",
    "OptionB": "3",
    "OptionC": "5",
    "OptionD": "6",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Distance from Center to Point",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "geometry/circles/distance"
  },
  {
    "Question": "If the equation of a circle is x² + y² - 6x + 8y + 9 = 0, what is the center of the circle?",
    "Answer": "B",
    "Explanation": "To find the center, rewrite the equation in standard form by completing the square. The center is (3, -4).",
    "PictureURL": "",
    "OptionA": "(6, -8)",
    "OptionB": "(3, -4)",
    "OptionC": "(3, 4)",
    "OptionD": "(6, 8)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Center from General Form",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "geometry/circles/center_general_form"
  },
  {
    "Question": "What is the equation of a circle with center at (-2, 3) and radius 7?",
    "Answer": "A",
    "Explanation": "Using the standard form, the equation is (x + 2)² + (y - 3)² = 49.",
    "PictureURL": "",
    "OptionA": "(x + 2)² + (y - 3)² = 49",
    "OptionB": "(x - 2)² + (y + 3)² = 49",
    "OptionC": "(x + 2)² + (y + 3)² = 7",
    "OptionD": "(x - 2)² + (y - 3)² = 49",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Circle Equation from Center and Radius",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "geometry/circles/equation_center_radius"
  },
  {
    "Question": "Which of the following points is NOT on the circle defined by (x - 1)² + (y - 1)² = 4?",
    "Answer": "D",
    "Explanation": "Substituting each point into the equation shows that (1, 5) does not satisfy the equation, while the others do.",
    "PictureURL": "",
    "OptionA": "(3, 1)",
    "OptionB": "(1, 3)",
    "OptionC": "(1, -1)",
    "OptionD": "(1, 5)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Identifying Points NOT on a Circle",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "geometry/circles/not_on_circle"
  },
  {
    "Question": "What is the radius of the circle represented by the equation x² + y² - 10x - 6y + 25 = 0?",
    "Answer": "B",
    "Explanation": "Rearranging the equation into standard form reveals the radius as √(25) = 5.",
    "PictureURL": "",
    "OptionA": "10",
    "OptionB": "5",
    "OptionC": "6",
    "OptionD": "25",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Radius from General Form",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "geometry/circles/radius_general_form"
  },
  {
    "Question": "What is the center of the circle given by the equation x² + y² + 4x - 2y - 8 = 0?",
    "Answer": "C",
    "Explanation": "Completing the square for both x and y gives the center as (-2, 1).",
    "PictureURL": "",
    "OptionA": "(2, -1)",
    "OptionB": "(2, 1)",
    "OptionC": "(-2, 1)",
    "OptionD": "(-2, -1)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Finding Center from General Form",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "geometry/circles/center_general_form"
  },
  {
    "Question": "Which of the following equations represents a circle with a radius of 3 and center at (0, 0)?",
    "Answer": "A",
    "Explanation": "The standard equation for a circle centered at the origin with radius 3 is x² + y² = 9.",
    "PictureURL": "",
    "OptionA": "x² + y² = 9",
    "OptionB": "x² + y² = 3",
    "OptionC": "(x - 0)² + (y - 0)² = 3",
    "OptionD": "(x + 0)² + (y + 0)² = 9",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Circles in Coordinate Plane",
    "Content Type": "Mathematics",
    "Title": "Circle Equation from Radius",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "geometry/circles/equation_radius"
  }
]