test","extracted_subject":"MATH","extracted_chapter":"CIRCLE AND SYSTEM OF CIRCLES","extracted_topic":"TANGENT AND NORMAL TO A CIRCLE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1801.png?top_left_x=0&top_left_y=363&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d9be","slug":"the-number-of-common-tangents-that-can-be-drawn-to","content":"The number of common tangents that can be drawn to the circles x²+y²–4x-6y-3 = 0 and x²+y²+2x+2y+1=0 is","options":[{"_id":"68a405557f15af4716c88b86","text":"1","sequence":0,"isCorrect":false},{"_id":"68a405557f15af4716c88b87","text":"2","sequence":1,"isCorrect":false},{"_id":"68a405557f15af4716c88b88","text":"3","sequence":2,"isCorrect":true},{"_id":"68a405557f15af4716c88b89","text":"4","sequence":3,"isCorrect":false}],"correct_answer":"3","explanation":"The two circles are\n\nx²+y²-4x-6y-3 = 0 and x²+y²+2x+2y+1 = 0\n\nCentres: C₁ ≡(2, 3), C₂ ≡(-1, -1)\n\nRadii: r₁ = 4 r₂ = 1\n\nWe have, C₁ C₂ = 5 = r₁ + r₂, therefore there are 3 common tangents to the given circles","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.916Z","__v":0,"vector_store_id":"776d3469-09e3-47ae-a99e-77542be30b65","updated_at":"2024-08-30T21:49:36.916Z","isStarred":false},"params":{"questionSlug":"the-number-of-common-tangents-that-can-be-drawn-to"}}]}]]

Question: The number of common tangents that can be drawn to the circles x<sup>2</sup>+y<sup>2</sup>–4x-6y-3 =...

Solution