st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"PARABOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1814.png?top_left_x=0&top_left_y=946&width=532&height=262&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31db56","slug":"the-circle-xsup2sup-ysup2sup-2lx-0-l-r-touches-the","content":"The circle x² + y² + 2lx = 0, lĪ R touches the parabola\n\ny² = 4x externally, then –","options":[{"_id":"68dfdbd08c3e555ae9e7db49","text":"l\\> 0","sequence":0,"isCorrect":true},{"_id":"68dfdbd08c3e555ae9e7db4a","text":"l\\< 0","sequence":1,"isCorrect":false},{"_id":"68dfdbd08c3e555ae9e7db4b","text":"l\\> 1","sequence":2,"isCorrect":false},{"_id":"68dfdbd08c3e555ae9e7db4c","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"l\\> 0","explanation":"Given equations x² + y² + 2lx = 0,\n\ny² = 4x centre of circle is (–l, 0) and radius is\n\n\\(\\sqrt { \\lambda ^ { 2 } + 0 }\\)= l.\n\nClearly the circle will touch the parabola exterenally if centre of circle lies on –ve x axis i.e. l \\> 0.\n\n![](https://cdn.pureessence.tech/canvas_124.png?top_left_x=0&top_left_y=1799&width=300&height=197)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.017Z","__v":0,"vector_store_id":"66147fb9-a84a-49bb-93fe-0dd97a2ab04e","updated_at":"2024-08-30T21:49:37.017Z","isStarred":false},"params":{"questionSlug":"the-circle-xsup2sup-ysup2sup-2lx-0-l-r-touches-the"}}]}]]

Question: The circle x<sup>2</sup> + y<sup>2</sup> + 2lx = 0, lĪ R touches the parabola y<sup>2</sup> = 4x ex...

Solution