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[
{
"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": ""
}
]
}
]