test","extracted_subject":"MATH","extracted_chapter":"CIRCLE AND SYSTEM OF CIRCLES","extracted_topic":"CHORD OF CONTACT OF TANGENT, POLE AND POLAR","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2255.png?top_left_x=0&top_left_y=377&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab321677","slug":"locus-of-centre-of-variable-circle-txsup2sup-tysup","content":"Locus of centre of variable circle tx² + ty² + 2(t² + 1)x – 2(t² –1)y – 5t = 0 is a :","options":[{"_id":"68aaced17f15af4716dd29ac","text":"Straight line","sequence":0,"isCorrect":false},{"_id":"68aaced17f15af4716dd29ad","text":"Circle","sequence":1,"isCorrect":false},{"_id":"68aaced17f15af4716dd29ae","text":"Parabola","sequence":2,"isCorrect":false},{"_id":"68aaced17f15af4716dd29af","text":"Hyperbola","sequence":3,"isCorrect":true}],"correct_answer":"Hyperbola","explanation":"Circle x² + y² +2\\(\\frac{(t^{2} + 1)}{t}\\)x – 2 \\(\\frac{(t^{2}–1)}{t}\\)y – 5 = 0\n\ncentre \\(\\left( –t–\\frac{1}{t},t–\\frac{1}{t} \\right)\\)\n\nlocus x² – y² = \\(\\left( t + \\frac{1}{t} \\right)^{2}\\) – \\(\\left( t–\\frac{1}{t} \\right)^{2}\\) = 4\n\nŽ Hyperbola","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.816Z","__v":0,"vector_store_id":"42ec34d8-941f-47fc-a660-39633fe63db1","updated_at":"2024-08-30T21:49:40.816Z","isStarred":false},"params":{"questionSlug":"locus-of-centre-of-variable-circle-txsup2sup-tysup"}}]}]]

Question: Locus of centre of variable circle tx<sup>2</sup> + ty<sup>2</sup> + 2(t<sup>2</sup> + 1)x – 2(t<sup...

Solution