st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"ELLIPSE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1832.png?top_left_x=1064&top_left_y=0&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31dde3","slug":"the-foci-of-the-ellipse-25-x-1sup2sup-9-y-2sup2sup","content":"The foci of the ellipse, 25 (x + 1)² + 9 (y + 2)²= 225 are at –","options":[{"_id":"68a3ee527f15af4716c7c8d8","text":"(–1, 2) and (–1, –6)","sequence":0,"isCorrect":true},{"_id":"68a3ee527f15af4716c7c8d9","text":"(–2, 1) & (–2, 6)","sequence":1,"isCorrect":false},{"_id":"68a3ee527f15af4716c7c8da","text":"(–1, –2) & (–2, –1)","sequence":2,"isCorrect":false},{"_id":"68a3ee527f15af4716c7c8db","text":"(–1, –2) & (–1, – 6)","sequence":3,"isCorrect":false}],"correct_answer":"(–1, 2) and (–1, –6)","explanation":"(x + 1)²/9 + (y + 2)²/25 = 1, a = 3 X=x+1 \\\\ b \\> a\n\nb=5Y=y+2\\foci=(0,±be),a²=b² (1–e²)9\n\n= 25 (1 – e²)\n\nŽe²=1–9/25Že=4/5\\\\0,± be)\n\nŽ(0±5(4/5)Ž(0,±4)\n\n\\X=0&Y = ± 4 x + 1 = 0 y + 2 = ± 4 (– 1, 2)\n\n& (–1, –6)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.173Z","__v":0,"vector_store_id":"81d3023c-0fc0-44ae-8198-b4ef23f21429","updated_at":"2024-08-30T21:49:37.173Z","isStarred":false},"params":{"questionSlug":"the-foci-of-the-ellipse-25-x-1sup2sup-9-y-2sup2sup"}}]}]]

Question: The foci of the ellipse, 25 (x + 1)<sup>2</sup> + 9 (y + 2)<sup>2</sup>= 225 are at –...

Solution