st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"ELLIPSE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1836.png?top_left_x=0&top_left_y=817&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31de7d","slug":"the-number-of-real-tangents-that-can-be-drawn-on-t","content":"The number of real tangents that can be drawn on the ellipse 3x² + 5y² = 32 and 25x² + 9y² = 450 passing through (3, 5) is:","options":[{"_id":"68a3ea4a7f15af4716c6e857","text":"0","sequence":0,"isCorrect":false},{"_id":"68a3ea4a7f15af4716c6e858","text":"2","sequence":1,"isCorrect":false},{"_id":"68a3ea4a7f15af4716c6e859","text":"3","sequence":2,"isCorrect":true},{"_id":"68a3ea4a7f15af4716c6e85a","text":"4","sequence":3,"isCorrect":false}],"correct_answer":"3","explanation":"Since 3 x 3² + 5 x 5² - 32 \\> 0, the point (3, 5) lies outside the ellipse 3x² _{+ 5y}² = 32.\n\nAlso, 25 x 3² + 0 x 5² - 450 = 0, ∴ the point (3, 5) lies on the ellipse 25x² + 9y² = 450. So the required number of tangents is 3.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.219Z","__v":0,"vector_store_id":"f39462b7-4a4e-4e16-a1cd-bc0d7cf0f46f","updated_at":"2024-08-30T21:49:37.219Z","isStarred":false},"params":{"questionSlug":"the-number-of-real-tangents-that-can-be-drawn-on-t"}}]}]]

Question: The number of real tangents that can be drawn on the ellipse 3x<sup>2</sup> + 5y<sup>2</sup> = 32 an...

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