Transcript: ellipse_20250808_071808.html

View and copy the extracted transcript JSON

Back to Files

Narration Generator

Generate narration from your transcript

Leave empty to use default narration settings. Use this to customize the narration approach.

[
  {
    "slide": 1,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Meet the Ellipse\nDiscover the shape behind orbits, tracks, and tunes.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 2,
    "fragments": [
      {
        "fragment_index": 1,
        "text_description": "Formal Definition",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Ellipse",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "An ellipse is the set of all points in a plane whose distances to two fixed points, called foci, always add to the same constant value.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Which everyday objects do you think satisfy this constant-sum rule?",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 3,
    "fragments": [
      {
        "fragment_index": 1,
        "text_description": "Focus on the Foci",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Ellipse with axes, centre and foci.",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/8oN0MnbUnXZVXr4TFdkcc6w3isKruNZnGBX84Q9E.png"
      },
      {
        "fragment_index": 3,
        "text_description": "Key Parts on the Diagram",
        "image_description": ""
      },
      {
        "fragment_index": -1,
        "text_description": "Label each part of the ellipse, then verify the focal rule.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Key Points:\nA, B: ends of the major axis, length \\(2a\\).\nC, D: ends of the minor axis, length \\(2b\\).\n\\(F_1, F_2\\): foci, symmetric about centre O.\nAny point \\(P\\) keeps \\(PF_1 + PF_2 = 2a\\).",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 4,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "The a² = b² + c² Link",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "\\[a^{2}=b^{2}+c^{2}\\]",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Variable Definitions\na\nSemi-major axis length\nb\nSemi-minor axis length\nc\nDistance from centre to a focus",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Applications\nLocate Foci\nUse \\(c=\\sqrt{a^{2}-b^{2}}\\) to plot focus points quickly.\nFind Eccentricity\nCompute \\(e=\\frac{c}{a}\\) to measure how “stretched” the ellipse is.\nVerify Ellipse Data\nCheck if given \\(a,b,c\\) satisfy the relation before graphing.\nSource: NCERT Class 11 Mathematics",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 5,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Two Orientations",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Major Axis Along x-axis\n\\( \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}} = 1,\\; a>b \\)\nLarger denominator under \\(x\\) → x-major orientation check\nFoci at \\((\\pm c,0)\\) with \\(c^{2}=a^{2}-b^{2}\\)\nVertices \\((\\pm a,0)\\); major axis length \\(2a\\)",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Major Axis Along y-axis\n\\( \\frac{x^{2}}{b^{2}}+\\frac{y^{2}}{a^{2}} = 1,\\; a>b \\)\nLarger denominator under \\(y\\) → y-major orientation check\nFoci at \\((0,\\pm c)\\) with \\(c^{2}=a^{2}-b^{2}\\)\nVertices \\((0,\\pm a)\\); major axis length \\(2a\\)",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Key Similarities\nCentre at \\((0,0)\\) for both orientations\nRelation \\(c^{2}=a^{2}-b^{2}\\) and eccentricity \\(e=\\frac{c}{a}\\)\nMinor axis length \\(2b\\) and the condition \\(a>b\\)",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 6,
    "fragments": []
  },
  {
    "slide": 7,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Multiple Choice Question\nSubmit Answer\nCorrect!\n\\( \\frac{4}{9}+\\frac{1}{4}= \\frac{25}{36} < 1 \\). Therefore, \\( P \\) is inside the ellipse.\nIncorrect\nPlug the coordinates into the equation. Compare the result with 1: <1 → inside, =1 → on, >1 → outside.\n// MCQ interaction logic\n        const correctOption = 0;\n        const answerCards = document.querySelectorAll('.answer-card');\n        const submitBtn = document.getElementById('submitBtn');\n        const feedbackCorrect = document.getElementById('feedbackCorrect');\n        const feedbackIncorrect = document.getElementById('feedbackIncorrect');\n        \n        let selectedOption = null;\n        \n        answerCards.forEach((card, index) => {\n            card.addEventListener('click', () => {\n                answerCards.forEach(c => c.classList.remove('border-blue-500', 'bg-blue-50'));\n                card.classList.add('border-blue-500', 'bg-blue-50');\n                selectedOption = index;\n            });\n        });\n        \n        submitBtn.addEventListener('click', () => {\n            if (selectedOption === null) return;\n            \n            if (selectedOption === correctOption) {\n                feedbackCorrect.classList.remove('hidden');\n                feedbackIncorrect.classList.add('hidden');\n            } else {\n                feedbackIncorrect.classList.remove('hidden');\n                feedbackCorrect.classList.add('hidden');\n            }\n        });",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Question\nFor the ellipse \\( \\frac{x^{2}}{9} + \\frac{y^{2}}{4} = 1 \\), the point \\( P(2,1) \\) lies\n                _____ the curve.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "1\nInside the ellipse",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "2\nOn the ellipse",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "3\nOutside the ellipse",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "4\nCannot be determined",
        "image_description": ""
      },
      {
        "fragment_index": 6,
        "text_description": "Hint:\nSubstitute \\( x = 2, y = 1 \\). Compare the sum with 1 to decide the location.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 8,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Key Takeaways\nEllipses in a nutshell",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Definition\nLocus of points whose distances to two fixed foci add to a constant.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Standard Formulas\nCentre at origin: \\( \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}} = 1 \\); focus distance \\(c\\) obeys \\(c^{2}=a^{2}-b^{2}\\).",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Orientation\nIf \\(a>b\\), major axis lies on x-axis; if \\(b>a\\), on y-axis; rotation introduces an \\(xy\\) term.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Parameter Effects\nIncreasing \\(a\\) widens, \\(b\\) tallens; larger \\(c\\) raises eccentricity \\(e=c/a\\).",
        "image_description": ""
      }
    ]
  }
]