[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523559-105":59,"doc-detail-523559-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","rotations-of-conic-sections-worksheet-classify-and-rotate-conic-equations","Rotations of Conic Sections - worksheet - classify and rotate conic equations","","Infinite Precalculus worksheet on rotations of conic sections. Students first classify each conic section in the rotated uv-plane form and identify the type (parabola, ellipse, or hyperbola) for multiple numbered items. The next tasks transform equations from the xy-plane to the rotated uv-plane, using a provided rotation angle, and rewrite them without cross-product terms when the angle must be determined.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/rotations-of-conic-sections-worksheet-classify-and-rotate-conic-equations/523559/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/rotations-of-conic-sections-worksheet-classify-and-rotate-conic-equations/523559.png","ImageObject",300,407,{"name":92,"@type":93},"acoobca","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main skill practiced in this worksheet?","Question",{"text":113,"@type":114},"Classifying conic sections and transforming their equations from the xy-plane to a rotated uv-plane.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do students handle the problem set where an angle of rotation is provided?",{"text":118,"@type":114},"They use the given rotation angle to rewrite each equation in the rotated uv-coordinates.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the worksheet ask students to do when the cross-product term must be eliminated?",{"text":122,"@type":114},"Determine a rotation angle between the stated limits and then transform the equation so the cross term is removed.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},523559,1791504546,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},3985747870733,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Precalculus Name   \nRotations of Conic Sections Date  Period   \nClassify each conic section.  \n1) 􀀐u􀀕 􀀎 􀀕 uv 􀀐 v 􀀕 􀀎 􀀕 􀂘 u 􀀎 􀀕 􀂘 v 􀀠 􀀓 2) 􀀖􀀚 u 􀀕 􀀎 􀀚􀀓 uv 􀀎 􀀖􀀚 v 􀀕 􀀐 􀀚􀀕 􀀠 􀀓  \n3) u 􀀕 􀀐 􀀔􀀗 uv 􀀎 v 􀀕 􀀐 􀀔􀀕􀀓 􀀠 􀀓 4) 􀀔􀀖 u 􀀕 􀀎 􀀔􀀓 uv 􀀎 􀀔􀀖 v 􀀕 􀀐 􀀕􀀛􀀛 􀀠 􀀓  \nTransform each equation from the xy-plane to the rotated uv-plane. The uv-plane's angle of rotation is provided.  \n5) x 􀀕 􀀎 y 􀀠 􀀓 , 􀁔 􀀠 􀀙􀀓􀁱 6) x 􀀕 􀀎 􀀗y 􀀕 􀀐 􀀖􀀙 􀀠 􀀓 , 􀁔 􀀠 􀀖􀀓􀁱  \n7) x 􀀕  􀀎  y 􀀕  􀀠 􀀔 􀁔 􀀠 􀀖􀀓􀁱 8) x 􀀕  􀀐 y 􀀕  􀀠 􀀔 􀁔 􀀠 􀀗􀀘􀁱􀀔􀀙 􀀖􀀙 , 􀀔􀀙 􀀔􀀙 ,  \nEliminate the cross-product term by determining an angle of rotation between 􀀓° and 􀀜􀀓° and transforming the equation from the xy-plane to the rotated uv-plane.  \n9) 􀀖􀀚x 􀀕 􀀎 􀀗􀀕 􀀖 􀂘 xy 􀀎 􀀚􀀜 y 􀀕 􀀐 􀀗􀀓􀀓 􀀠 􀀓 10) 􀀔􀀔 x 􀀕 􀀎 􀀔􀀓 􀀖 􀂘 xy 􀀎 y 􀀕 􀀐 􀀙􀀗 􀀠 􀀓  \nKuta Software-Infinite Precalculus Name   \nRotations of Conic Sections Date  Period   \nClassify each conic section.  \n1) 􀀐u􀀕 􀀎 􀀕 uv 􀀐 v 􀀕 􀀎 􀀕 􀂘 u 􀀎 􀀕 􀂘 v 􀀠 􀀓 2) 􀀖􀀚 u 􀀕 􀀎 􀀚􀀓 uv 􀀎 􀀖􀀚 v 􀀕 􀀐 􀀚􀀕 􀀠 􀀓  \nParabola Ellipse  \n3) u 􀀕 􀀐 􀀔􀀗 uv 􀀎 v 􀀕 􀀐 􀀔􀀕􀀓 􀀠 􀀓 4) 􀀔􀀖 u 􀀕 􀀎 􀀔􀀓 uv 􀀎 􀀔􀀖 v 􀀕 􀀐 􀀕􀀛􀀛 􀀠 􀀓  \nHyperbola Ellipse  \nTransform each equation from the xy-plane to the rotated uv-plane. The uv-plane's angle of rotation is provided.  \n5) x 􀀕 􀀎 y 􀀠 􀀓 , 􀁔 􀀠 􀀙􀀓􀁱 6) x 􀀕 􀀎 􀀗y 􀀕 􀀐 􀀖􀀙 􀀠 􀀓 , 􀁔 􀀠 􀀖􀀓􀁱  \nu 􀀕 􀀐 􀀕 􀀖 􀂘 uv 􀀎 􀀖 v 􀀕 􀀎 􀀕 􀀖 􀂘 u 􀀎 􀀕 v 􀀠 􀀓 􀀚u􀀕 􀀎 􀀙 􀀖 􀂘 uv 􀀎 􀀔􀀖 v 􀀕 􀀐 􀀔􀀗􀀗 􀀠 􀀓  \n7) x 􀀕  􀀎  y 􀀕  􀀠 􀀔 􀁔 􀀠 􀀖􀀓􀁱 8) x 􀀕  􀀐 y 􀀕  􀀠 􀀔 􀁔 􀀠 􀀗􀀘􀁱  \n􀀔􀀙 􀀖􀀙 , 􀀔􀀙 􀀔􀀙 ,  \n􀀖􀀔 u 􀀕 􀀐 􀀔􀀓 􀀖 􀂘 uv 􀀎 􀀕􀀔 v 􀀕 􀀐 􀀘􀀚􀀙 􀀠 􀀓 􀀐􀀕 uv 􀀐 􀀔􀀙 􀀠 􀀓  \nEliminate the cross-product term by determining an angle of rotation between 􀀓° and 􀀜􀀓° and transforming the equation from the xy-plane to the rotated uv-plane.  \n9) 􀀖􀀚x 􀀕 􀀎 􀀗􀀕 􀀖 􀂘 xy 􀀎 􀀚􀀜 y 􀀕 􀀐 􀀗􀀓􀀓 􀀠 􀀓  \n􀀕􀀘 u 􀀕 􀀎 􀀗v 􀀕 􀀐 􀀔􀀓􀀓 􀀠 􀀓 , 􀁔 􀀠 􀀙􀀓􀁱  \n10) 􀀔􀀔 x 􀀕 􀀎 􀀔􀀓 􀀖 􀂘 xy 􀀎 y 􀀕 􀀐 􀀙􀀗 􀀠 􀀓  \n􀀗 u 􀀕 􀀐 v 􀀕 􀀐 􀀔􀀙 􀀠 􀀓 , 􀁔 􀀠 􀀖􀀓􀁱  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiaF3nhOADmr9","https://ap.wps.com/l/cbCaiaF3nhOADmr9","pdf",24055,"English","# Classify each conic section\n# Transform equations from the xy-plane to the rotated uv-plane\n# Eliminate the cross-product term by choosing a rotation angle","[{\"question\":\"What is the main skill practiced in this worksheet?\",\"answer\":\"Classifying conic sections and transforming their equations from the xy-plane to a rotated uv-plane.\"},{\"question\":\"How do students handle the problem set where an angle of rotation is provided?\",\"answer\":\"They use the given rotation angle to rewrite each equation in the rotated uv-coordinates.\"},{\"question\":\"What does the worksheet ask students to do when the cross-product term must be eliminated?\",\"answer\":\"Determine a rotation angle between the stated limits and then transform the equation so the cross term is removed.\"}]","Rotations of Conic Sections - worksheet - classify and rotate conic equations | PDF",1791427013]