st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"PARABOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1818.png?top_left_x=1064&top_left_y=562&width=532&height=212&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31dc0b","slug":"the-locus-of-the-poles-of-the-focal-chords-of-a-pa","content":"The locus of the poles of the focal chords of a parabola is","options":[{"_id":"68a3d6187f15af4716c57d74","text":"The directrix of the parabola","sequence":0,"isCorrect":false},{"_id":"68a3d6187f15af4716c57d75","text":"A focal chord of the parabola","sequence":1,"isCorrect":false},{"_id":"68a3d6187f15af4716c57d76","text":"The axis of the parabola","sequence":2,"isCorrect":false},{"_id":"68a3d6187f15af4716c57d77","text":"The tangent at the vertex of the parabola","sequence":3,"isCorrect":true}],"correct_answer":"The tangent at the vertex of the parabola","explanation":"Let (x₁, y₁) be the pole.\n\nPolar of (x₁, y₁) w.r.to the parabola is S₁= 0\n\nyy₁ – 2a(x+x₁) =0\n\nthis passes through the focus (a, 0)\n\nthen 0.y₁ – 2a(0+x₁) = 0\n\n⇒ x₁ = 0\n\n∴ locus of (x₁ y₁) is x = 0 which is the tangent at the vertex.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.066Z","__v":0,"vector_store_id":"77dee33b-4e57-48c3-9e0d-13302e76bdd6","updated_at":"2024-08-30T21:49:37.066Z","isStarred":false},"params":{"questionSlug":"the-locus-of-the-poles-of-the-focal-chords-of-a-pa"}}]}]]

Question: The locus of the poles of the focal chords of a parabola is...

Solution