st","extracted_subject":"MATH","extracted_chapter":"CIRCLE AND SYSTEM OF CIRCLES","extracted_topic":"EQUATIONS OF CIRCLE, GEOMETRICAL PROBLEMS REGARDING CIRCLE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1790.png?top_left_x=532&top_left_y=1647&width=532&height=265&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d834","slug":"if-circles-xsup2sup-ysup2sup-3x-ly-5-0-and-4xsup2s","content":"If circles x² + y² – 3x + ly – 5 = 0 and 4x² + 4y² – 12x + y – 9 = 0 are concentric then l equals","options":[{"_id":"68a3944c7f15af4716ba3677","text":"\$\\frac{1}{4}\$","sequence":0,"isCorrect":true},{"_id":"68a3944c7f15af4716ba3678","text":"\$- \\frac{1}{4}\$","sequence":1,"isCorrect":false},{"_id":"68a3944c7f15af4716ba3679","text":"\$\\frac{1}{8}\$","sequence":2,"isCorrect":false},{"_id":"68a3944c7f15af4716ba367a","text":"\$- \\frac{1}{8}\$","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac{1}{4}$","explanation":"x² + y² – 3x + ly – 5 = 0 ̃ centre º (3/2, –l/2)\n\nx² + y² – 3x + \$\\frac{1}{4}\$y – \$\\frac{9}{4}\$ = 0 ̃ centre º \$\\left( \\frac{3}{2}, - \\frac{1}{8} \\right)\$\n\n\\\\ l = \$\\frac{1}{4}\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.816Z","__v":0,"vector_store_id":"e51eac24-428b-42e8-8423-00e188ee9932","updated_at":"2024-08-30T21:49:36.816Z","isStarred":false},"params":{"questionSlug":"if-circles-xsup2sup-ysup2sup-3x-ly-5-0-and-4xsup2s"}}]}]]

Question: If circles x<sup>2</sup> + y<sup>2</sup> – 3x + ly – 5 = 0 and 4x<sup>2</sup> + 4y<sup>2</sup> – 12x...

Solution