test","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"PARABOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1820.png?top_left_x=532&top_left_y=740&width=532&height=270&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31dc3e","slug":"the-straight-line-y-2x-l-does-not-meet-the-parabol","content":"The straight line y = 2x + l does not meet the parabola\n\ny² = 2x, if","options":[{"_id":"68a3b0d37f15af4716bf100b","text":"l\\<\$\\frac{1}{4}\$","sequence":0,"isCorrect":false},{"_id":"68a3b0d37f15af4716bf100c","text":"l\\>\$\\frac{1}{4}\$","sequence":1,"isCorrect":true},{"_id":"68a3b0d37f15af4716bf100d","text":"l = 4","sequence":2,"isCorrect":false},{"_id":"68a3b0d37f15af4716bf100e","text":"l = 1","sequence":3,"isCorrect":false}],"correct_answer":"l\\>$\\frac{1}{4}$","explanation":"line y = 2x + l …(i)\n\nParabola y² = 2x …(ii)\n\nFrom (i) & (ii) (2x+ l)² = 2x\n\ñ 4x² + 4xl + l² = 2x\n\ñ 4x² + 2x(2l – 1) + l² = 0\n\nDoes not meet the parabola D \\< 0\n\ñ 4(2l – 1)² – 4(4)(l²) \\< 0\n\ñ 4[4l² + 1 – 4l – 4l²] \\< 0\n\ñ 1 – 4l \\< 0 ̃ l \\> ¼","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.071Z","__v":0,"vector_store_id":"f2dbd6b4-2069-4920-bdc9-6518a79276f8","updated_at":"2024-08-30T21:49:37.071Z","isStarred":false},"params":{"questionSlug":"the-straight-line-y-2x-l-does-not-meet-the-parabol"}}]}]]

Question: The straight line y = 2x + l does not meet the parabola y<sup>2</sup> = 2x, if...

Solution