test","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"HYPERBOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1855.png?top_left_x=1064&top_left_y=1444&width=532&height=255&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31e0e3","slug":"if-the-normal-to-the-hyperbola-xy-csup2sup-at-the-","content":"If the normal to the hyperbola xy = c² at the point t₁ meets the curve again at the point t₂ then t₁t₂ equals.","options":[{"_id":"68aab4267f15af4716dba66a","text":"-1","sequence":0,"isCorrect":true},{"_id":"68aab4267f15af4716dba66b","text":"\\(- t_{1}^{- 2}\\)","sequence":1,"isCorrect":false},{"_id":"68aab4267f15af4716dba66c","text":"1/t₁","sequence":2,"isCorrect":false},{"_id":"68aab4267f15af4716dba66d","text":"1","sequence":3,"isCorrect":false}],"correct_answer":"-1","explanation":"Normal at P (ct₁, c/t₁) is \\(c{t_{1}}^{3} - yt_{1} - c{t_{1}}^{4} + c = 0\\).\n\nIf it passes through Q (ct₂, c/t₂), then\n\n\\(ct_{2}{t_{1}}^{3} - \\frac{ct_{1}}{t_{2}} - c{t_{1}}^{4} + c = 0\\).\n\nOn simplification, we get t₁t₂ = -1.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.372Z","__v":0,"vector_store_id":"e8ccc169-0374-4b5a-bc88-767d13066dbd","updated_at":"2024-08-30T21:49:37.372Z","isStarred":false},"params":{"questionSlug":"if-the-normal-to-the-hyperbola-xy-csup2sup-at-the-"}}]}]]

Question: If the normal to the hyperbola xy = c<sup>2</sup> at the point t<sub>1</sub> meets the curve again a...

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