st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"PARABOLA","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1812.png?top_left_x=0&top_left_y=1107&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31db49","slug":"the-locus-of-the-point-of-intersection-of-the-tang-1","content":"The locus of the point of intersection of the tangents to the parabola x² – 4x – 8y + 28 = 0 which are at right angles is","options":[{"_id":"68a3cdfa7f15af4716c3c4a8","text":"y = 0","sequence":0,"isCorrect":false},{"_id":"68a3cdfa7f15af4716c3c4a9","text":"y = –1","sequence":1,"isCorrect":false},{"_id":"68a3cdfa7f15af4716c3c4aa","text":"x = 1","sequence":2,"isCorrect":false},{"_id":"68a3cdfa7f15af4716c3c4ab","text":"y = 1","sequence":3,"isCorrect":true}],"correct_answer":"y = 1","explanation":"Locus of point of intersection of ^ tangent\n\n(i) Directrix\n\nx² – 4x – 8y + 28 = 0\n\nŽ x² – 4x = 8y – 28\n\nŽ x² – 4x + 4 = 8y – 28 + 4\n\n(x – 2)² = 8(y – 3)\n\nŽ X² = 8Y\n\n![](https://cdn.pureessence.tech/canvas_107.png?top_left_x=962&top_left_y=600&width=300&height=155)\n\nDirectrix\n\nY = – 2\n\nŽ y – 3 = – 2\n\ny = 1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.016Z","__v":0,"vector_store_id":"bbca294e-5192-41f1-8512-e5bfe6068201","updated_at":"2024-08-30T21:49:37.016Z","isStarred":false},"params":{"questionSlug":"the-locus-of-the-point-of-intersection-of-the-tang-1"}}]}]]

Question: The locus of the point of intersection of the tangents to the parabola x<sup>2</sup> – 4x – 8y + 28 ...

Solution