st","extracted_subject":"MATH","extracted_chapter":"DIFFRENTIATION AND APPLICATIONS OF DERIVATIVES","extracted_topic":"ROLLE'S THEOREM, LAGRANGE'S MEAN VALUE THEOREM","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1665.png?top_left_x=532&top_left_y=0&width=532&height=620&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e6f425d76b7ab31c857","slug":"the-sum-of-the-intercepts-made-by-a-tangent-to-the","content":"The sum of the intercepts made by a tangent to the curve\n\n\$\\sqrt{x}\$ +\$\\sqrt{y}\$ = 4 at point (4, 4) pm coordinate axes is –","options":[{"_id":"68a387e67f15af4716b81f8b","text":"4\$\\sqrt{2}\$","sequence":0,"isCorrect":false},{"_id":"68a387e67f15af4716b81f8c","text":"3\$\\sqrt{3}\$","sequence":1,"isCorrect":false},{"_id":"68a387e67f15af4716b81f8d","text":"8\$\\sqrt{2}\$","sequence":2,"isCorrect":false},{"_id":"68a387e67f15af4716b81f8e","text":"\$\\sqrt{256}\$","sequence":3,"isCorrect":true}],"correct_answer":"$$\\sqrt{256}$","explanation":"Let xⁿ + yⁿ = aⁿ at (x₁, y₁), then tangent is\n\n\$\\frac{x}{x_{1}^{1 - n}}\$ + \$\\frac{y}{y_{1}^{1 - n}}\$ = aⁿ\n\nIntercepts are x₁^1–n. aⁿ and y₁^1–n . aⁿ","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:35.779Z","__v":0,"vector_store_id":"5945f397-e394-4c52-87f9-bdb83d7470c0","updated_at":"2024-08-30T21:49:35.779Z","isStarred":false},"params":{"questionSlug":"the-sum-of-the-intercepts-made-by-a-tangent-to-the"}}]}]]

Question: The sum of the intercepts made by a tangent to the curve \(\sqrt{x}\) +\(\sqrt{y}\) = 4 at point (4...

Solution