st","extracted_subject":"MATH","extracted_chapter":"STRAIGHT LINES","extracted_topic":"ANGLE BETWEEN TWO STRAIGHT LINES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1772.png?top_left_x=1064&top_left_y=1093&width=532&height=259&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d5cb","slug":"if4asup2sup-9bsup2sup-csup2sup-12ab-0-then-the-fam","content":"If4a² + 9b² – c² + 12ab = 0, then the family of straight lines\n\nax + by + c = 0 is concurrent at :","options":[{"_id":"68a408317f15af4716c93d07","text":"(2, 3) or (–2, – 3)","sequence":0,"isCorrect":true},{"_id":"68a408317f15af4716c93d08","text":"(2, 3) or (2, – 3)","sequence":1,"isCorrect":false},{"_id":"68a408317f15af4716c93d09","text":"(–2, 3) or (–2, –3)","sequence":2,"isCorrect":false},{"_id":"68a408317f15af4716c93d0a","text":"(– 2, 3) or (2, – 3)","sequence":3,"isCorrect":false}],"correct_answer":"(2, 3) or (–2, – 3)","explanation":"ince 4a² + 9b² – c² + 12ab = 0\n\nŽ (2a + 3b)² – c² = 0\n\nŽ (2a + 3b + c) (2a + 3b – c) = 0\n\nŽ 2a + 3b + c = 0\n\nor 2a + 3b – c = 0\n\nŽ – 2a – 3b + c = 0\n\n\\\\ ax + by + c is concurrent at\n\n(2, 3) or (– 2, – 3)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.664Z","__v":0,"vector_store_id":"56ae964a-9837-495f-8a40-5e36a30bc9ee","updated_at":"2024-08-30T21:49:36.664Z","isStarred":false},"params":{"questionSlug":"if4asup2sup-9bsup2sup-csup2sup-12ab-0-then-the-fam"}}]}]]

Question: If4a<sup>2</sup> + 9b<sup>2</sup> – c<sup>2</sup> + 12ab = 0, then the family of straight lines ax ...

Solution