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_1791.png?top_left_x=0&top_left_y=312&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d83a","slug":"if-the-circles-xsup2sup-ysup2sup-2x-2ky-6-0-and-xs","content":"If the circles x² + y² + 2x + 2ky + 6 = 0 and x² + y² + 2ky + k = 0 intersect orthogonally. then k is","options":[{"_id":"68a3d4327f15af4716c53c92","text":"2 or – 3/2","sequence":0,"isCorrect":true},{"_id":"68a3d4327f15af4716c53c93","text":"–2 or – 3/2","sequence":1,"isCorrect":false},{"_id":"68a3d4327f15af4716c53c94","text":"2 or 3/2","sequence":2,"isCorrect":false},{"_id":"68a3d4327f15af4716c53c95","text":"– 2 or 3/2","sequence":3,"isCorrect":false}],"correct_answer":"2 or – 3/2","explanation":"Use 2g₁g₂ + 2f₁f₂ = c₁ + c₂\n\n{If two circle cuts orthogonally}\n\n= 2 × 1 × 0 + 2. k × k = 6 + k\n\ñ 2k² – k – 6 = 0\n\ñ 2k² – 4k + 3k – 6 = 0\n\ñ 2k(k – 2) + 3(k – 2) = 0\n\ñ (2k+ 3)(k – 2) = 0\n\ñ k = – 3/2, 2","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.816Z","__v":0,"vector_store_id":"034830bf-96d5-4c12-a363-a6c03ce2e609","updated_at":"2024-08-30T21:49:36.816Z","isStarred":false},"params":{"questionSlug":"if-the-circles-xsup2sup-ysup2sup-2x-2ky-6-0-and-xs"}}]}]]

Question: If the circles x<sup>2</sup> + y<sup>2</sup> + 2x + 2ky + 6 = 0 and x<sup>2</sup> + y<sup>2</sup> + ...

Solution