st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"HYPERBOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1851.png?top_left_x=0&top_left_y=866&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31e033","slug":"the-locus-of-the-middle-points-of-chords-of-hyperb","content":"The locus of the middle points of chords of hyperbola 3x² – 2y² + 4x – 6y = 0 parallel to y = 2x is","options":[{"_id":"68dfdae98c3e555ae9e7ab6a","text":"3x – 4y = 4","sequence":0,"isCorrect":true},{"_id":"68dfdae98c3e555ae9e7ab6b","text":"3y – 4x + 4 = 0","sequence":1,"isCorrect":false},{"_id":"68dfdae98c3e555ae9e7ab6c","text":"4x – 4y = 3","sequence":2,"isCorrect":false},{"_id":"68dfdae98c3e555ae9e7ab6d","text":"3x – 4y = 2","sequence":3,"isCorrect":false}],"correct_answer":"3x – 4y = 4","explanation":"Let mid point be (h, k). Equation of a chord whose mid point is (h, k) would be T = S₁\n\nor 3xh – 2yk + 2(x + h) – 3(y + k) = 3h² – 2k² + 4h – 6k\n\n⇒ x(3k + 2) – y(2k + 3) – 2h + 3k – 3h² + 2k² = 0.\n\nIt’s slope is \\(\\frac{3h + 2}{2k + 3} = 2\\) (given)\n\n⇒ 3h = 4k + 4.\n\n⇒ Required locus is 3x – 4y = 4","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.321Z","__v":0,"vector_store_id":"86fa4ebb-8dbc-4600-b033-1452ece96ec9","updated_at":"2024-08-30T21:49:37.321Z","isStarred":false},"params":{"questionSlug":"the-locus-of-the-middle-points-of-chords-of-hyperb"}}]}]]

Question: The locus of the middle points of chords of hyperbola 3x<sup>2</sup> – 2y<sup>2</sup> + 4x – 6y = 0 ...

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