test","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"HYPERBOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1856.png?top_left_x=0&top_left_y=1018&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31e0ec","slug":"the-locus-of-a-point-p-moving-under-the-condition-","content":"The locus of a point P(α, β) moving under the condition that the line y = ax + β is a tangent to the hyperbola \\(\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}}\\) = 1 is","options":[{"_id":"68a3727d7f15af4716b4875c","text":"A parabola","sequence":0,"isCorrect":false},{"_id":"68a3727d7f15af4716b4875d","text":"A hyperbola","sequence":1,"isCorrect":true},{"_id":"68a3727d7f15af4716b4875e","text":"An ellipse","sequence":2,"isCorrect":false},{"_id":"68a3727d7f15af4716b4875f","text":"A circle","sequence":3,"isCorrect":false}],"correct_answer":"A hyperbola","explanation":"If y = mx + c is tangent to the hyperbola then\n\nc² = a² m² – b². Here β² = a²α² – b². Hence locus of P(α, β) is a²x² – y² = b², which is a hyperbola.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.373Z","__v":0,"vector_store_id":"ad78922e-0c01-4e57-9599-36aa6213fc9f","updated_at":"2024-08-30T21:49:37.373Z","isStarred":false},"params":{"questionSlug":"the-locus-of-a-point-p-moving-under-the-condition-"}}]}]]

Question: The locus of a point P(α, β) moving under the condition that the line y = ax + β is a tangent to the...

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