[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523558-105":59,"doc-detail-523558-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","ellipses-infinite-precalculus-worksheet","Ellipses - Infinite Precalculus Worksheet","","Infinite Precalculus ellipses worksheet for identifying key ellipse features and graphing each case. It guides learners to locate the center, vertices, co-vertices, and foci, then extends to compute major-axis length, minor-axis length, latus rectum length, and eccentricity. Additional items require using the given points and dimensions to write standard form equations of ellipses, supporting both conceptual understanding and procedural practice.",{"@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/ellipses-infinite-precalculus-worksheet/523558/",{"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/ellipses-infinite-precalculus-worksheet/523558.png","ImageObject",300,407,{"name":92,"@type":93},"CatatanPagi","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 ellipse elements does the worksheet ask you to identify first?","Question",{"text":113,"@type":114},"For each ellipse, it asks for the center, vertices, co-vertices, and foci, and then to sketch the graph based on them.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Besides vertices and foci, what additional measurements are required?",{"text":118,"@type":114},"It requires the length of the major axis, length of the minor axis, length of the latus rectum, and the eccentricity for each ellipse.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the final task after collecting the information?",{"text":122,"@type":114},"The worksheet asks you to use the provided information to write the standard form equation of each ellipse.","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},523558,1791536313,{"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":19,"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":52,"preview_page_count":4},962090894170,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Precalculus Name   \nEllipses Date  Period   \nIdentify the center, vertices, co-vertices, and foci of each. Then sketch the graph.  \n1) (x~~ ~~􀀖)􀀕 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀔)􀀕 􀀠 􀀔  \n3) (x~~ ~~~~ ~~􀀔)􀀕 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀘~~ ~~)~~ ~~􀀕 􀀠 􀀔  \n5) x 􀀕 􀀎 􀀜 y 􀀕 􀀎 􀀙x 􀀐 􀀜􀀓y 􀀎 􀀕􀀕􀀘 􀀠 􀀓  \n2) (x~~ ~~~~ ~~􀀖)􀀕 􀀎 ~~ ~~(y~~ ~~􀀔)􀀕 􀀠 􀀔  \n4) 􀀕􀀜 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀖)􀀕 􀀠 􀀔  \n6) 􀀜x 􀀕 􀀎 􀀗y 􀀕 􀀐 􀀖􀀙x 􀀎 􀀕􀀗y 􀀎 􀀖􀀙 􀀠 􀀓  \nIdentify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis, length of the latus rectum, and eccentricity of each.  \n7) 􀀖 x 􀀕 􀀎 􀀖􀀘 y 􀀕 􀀐 􀀙􀀓x 􀀎 􀀔􀀗􀀓y 􀀐 􀀛􀀘 􀀠 􀀓 8) 􀀖􀀙x 􀀕 􀀎 􀀘 y􀀕 􀀐 􀀜􀀓y 􀀐 􀀗􀀜􀀘 􀀠 􀀓  \nUse the information provided to write the standard form equation of each ellipse.  \n9) Vertices: (􀀙 , 􀀐􀀙), (􀀐􀀔􀀓 , 􀀐􀀙) 10) Vertices: (􀀔􀀖 , 􀀜), (􀀐􀀖 , 􀀜)  \nFoci: (􀀐􀀕 􀀎 􀀕 􀀚 , 􀀐􀀙), (􀀐􀀕 􀀐 􀀕 􀀚 , 􀀐􀀙) Foci: (􀀘 􀀎 􀀕 􀀚 , 􀀜), (􀀘 􀀐 􀀕 􀀚 , 􀀜)  \n11) VeCor-ceserti:c􀀘s,: 􀀐),􀀗(,􀀐􀀔􀀔􀀖􀀗),, 􀀐) 􀀗 , 􀀗) 12) FCooc-ei,c:􀀎( 􀀔 􀀔 ,􀀔􀀓􀀘􀀔􀀓)),,(􀀘,, 􀀔􀀓􀀔􀀓 􀀐) 􀀔􀀓􀀘 )  \n13) FociEndp: o(􀀗ints~~ ~~􀀖􀀘􀀕of~~ ~~􀀎mi􀀚no, a)x, i(:~~ ~~􀀗(~~ ~~􀀚􀀕~~ ~~,􀀖􀀘􀀕􀀚􀀕)􀀎,(􀀚􀀚􀀕,, ~~ ~~)􀀔􀀕 ) 14) CeVeFonterrtexcus:::(((􀀐􀀛􀀐􀀛􀀐􀀛,,,􀀘􀀔􀀘􀀘􀀎) ) 􀀘􀀔 )  \n15) Eni,)o, f(aj􀀙o,is: 16) Eccentricity = ~~ ~~􀀔􀀘􀀗~~  ~~Enin􀀓,t)f, m(r,is􀀓): CeCon-tveerr:te(:􀀘 􀀛) , 􀀘 )  \nKuta Software-Infinite Precalculus Name   \nEllipses Date  Period   \nIdentify the center, vertices, co-vertices, and foci of each. Then sketch the graph.  \n1) (x~~ ~~􀀖)􀀕 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀔)􀀕 􀀠 􀀔  \n3) (x~~ ~~~~ ~~􀀔)􀀕 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀘~~ ~~)~~ ~~􀀕 􀀠 􀀔  \n5) x 􀀕 􀀎 􀀜 y 􀀕 􀀎 􀀙x 􀀐 􀀜􀀓y 􀀎 􀀕􀀕􀀘 􀀠 􀀓  \n2) (x~~ ~~~~ ~~􀀖)􀀕 􀀎 ~~ ~~(y~~ ~~􀀔)􀀕 􀀠 􀀔  \n4) 􀀕􀀜 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀖)􀀕 􀀠 􀀔  \n6) 􀀜x 􀀕 􀀎 􀀗y 􀀕 􀀐 􀀖􀀙x 􀀎 􀀕􀀗y 􀀎 􀀖􀀙 􀀠 􀀓  \nIdentify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis,  \nlength of the latus rectum, and eccentricity of each.  \n7) 􀀖 x 􀀕 􀀎 􀀖􀀘 y 􀀕 􀀐 􀀙􀀓x 􀀎 􀀔􀀗􀀓y 􀀐 􀀛􀀘 􀀠 􀀓  \nCenter: (􀀔􀀓 , 􀀐􀀕)  \nVertices: (􀀔􀀓 􀀎 􀀘 􀀚 , 􀀐􀀕), (􀀔􀀓 􀀐 􀀘 􀀚 , 􀀐􀀕)  \nCo-vertices: (􀀔􀀓 , 􀀐􀀕 􀀎 􀀔􀀘 ), (􀀔􀀓 , 􀀐􀀕 􀀐 􀀔􀀘 )  \nFoci: (􀀔􀀓 􀀎 􀀗 􀀔􀀓 , 􀀐􀀕), (􀀔􀀓 􀀐 􀀗 􀀔􀀓 , 􀀐􀀕)  \nMajor Axis: 􀀔􀀓 􀀚 units  \nMinor Axis: 􀀕 􀀔􀀘 units  \nLatus Rectum: ~~ ~~􀀙~~ ~~􀀚~~ ~~ units  \nEccentricity: 􀀗~~ ~~􀀖~~ ~~􀀚􀀘􀀓~~ ~~ 􀁼 􀀓􀀑􀀜􀀘􀀙  \n8) 􀀖􀀙x 􀀕 􀀎 􀀘 y􀀕 􀀐 􀀜􀀓y 􀀐 􀀗􀀜􀀘 􀀠 􀀓  \nCenter: (􀀓 , 􀀜)  \nVertices: (􀀓 , 􀀜 􀀎 􀀙 􀀘 ), (􀀓 , 􀀜 􀀐 􀀙 􀀘 )  \nCo-vertices: (􀀘 , 􀀜), (􀀐􀀘 , 􀀜)  \nFoci: (􀀓 , 􀀜 􀀎 􀀔􀀘􀀘 ), (􀀓 , 􀀜 􀀐 􀀔􀀘􀀘 )  \nMajor Axis: 􀀔􀀕 􀀘 units  \nMinor Axis: 􀀔􀀓 units  \nLatus Rectum: ~~ ~~􀀘􀀖􀀖􀀔~~ ~~ units  \nEccentricity:  􀀙  􀁼 􀀓􀀑􀀜􀀕􀀛  \nUse the information provided to write the standard form equation of each ellipse.  \n9) Vertices: (􀀙 , 􀀐􀀙), (􀀐􀀔􀀓 , 􀀐􀀙)  \nFoci: (􀀐􀀕 􀀎 􀀕 􀀚 , 􀀐􀀙), (􀀐􀀕 􀀐 􀀕 􀀚 , 􀀐􀀙)  \n~~ ~~(x~~ ~~􀀗􀀕~~ ~~)~~ ~~􀀕 􀀎 ~~ ~~(y~~ ~~􀀙􀀙)􀀕 􀀠 􀀔  \n11) Vertices: (􀀘 , 􀀜), (􀀐􀀔􀀖 , 􀀜)  \nCo-vertices: (􀀐􀀗 , 􀀔􀀗), (􀀐􀀗 , 􀀗)  \n~~ ~~(x~~ ~~􀀗)􀀕 􀀎 ~~ ~~(y~~ ~~􀀘􀀜)􀀕 􀀠 􀀔  \n13) FociEndp: o(􀀗ints~~ ~~􀀖􀀘􀀕of~~ ~~􀀎mi􀀚no, a)x, i(:~~ ~~􀀗(~~ ~~􀀚􀀕~~ ~~,􀀖􀀘􀀕􀀚􀀕)􀀎,(􀀚􀀚􀀕,, ~~ ~~)􀀔􀀕 )  \n x 􀀐 􀀚􀀕~~ ~~) 􀀕 􀀎 (y 􀀐 􀀖􀀕~~ ~~) 􀀕 􀀠 􀀔  \n(  \n􀀔􀀗􀀗 􀀗  \n15) Endpoints of major axis:(􀀐􀀗 , 􀀐􀀙), (􀀐􀀔􀀙 , 􀀐􀀙)  \nEndpoints of minor axis:(􀀐􀀔􀀓 , 􀀐􀀕), (􀀐􀀔􀀓 , 􀀐􀀔􀀓)  \n~~ ~~(x~~ ~~~~ ~~􀀔􀀙~~ ~~􀀓)􀀕 􀀎 ~~ ~~(y~~ ~~􀀙)􀀕 􀀠 􀀔  \n10) Vertices: (􀀔􀀖 , 􀀜), (􀀐􀀖 , 􀀜)  \nFoci: (􀀘 􀀎 􀀕 􀀚 , 􀀜), (􀀘 􀀐 􀀕 􀀚 , 􀀜)  \n~~ ~~(x~~ ~~􀀗􀀘~~ ~~)~~ ~~􀀕 􀀎 ~~ ~~(y~~ ~~􀀙􀀜)􀀕 􀀠 􀀔  \n12) Foci: (􀀖 , 􀀔􀀓 􀀎 􀀔􀀓􀀘 ), (􀀖 , 􀀔􀀓 􀀐 􀀔􀀓􀀘 )  \nCo-vertices: (􀀔􀀔 , 􀀔􀀓), (􀀐􀀘 , 􀀔􀀓)  \n~~ ~~(x~~ ~~􀀗􀀖~~ ~~)~~ ~~􀀕 􀀎 ~~ ~~(y~~ ~~􀀔􀀜􀀓)􀀕 􀀠 􀀔  \n14) Center: (􀀐􀀛 , 􀀘 )  \nVertex: (􀀐􀀛 , 􀀔􀀘)  \nFocus: (􀀐􀀛 , 􀀘 􀀎 􀀘􀀔 )  \n~~ ~~(x~~ ~~􀀜􀀛)􀀕 􀀎 ~~ ~~(y~~ ~~􀀔􀀘􀀓)~~ ~~􀀕 􀀠 􀀔  \n16) Eccentricity = ~~ ~~􀀔􀀘􀀗~~  ~~Center: (􀀐􀀘 , 􀀘 )  \nCo-vertex: (􀀐􀀛 , 􀀘 )  \n~~ ~~(x~~ ~~~~ ~~􀀘~~ ~~)~~ ~~􀀕 􀀎 ~~ ~~(y~~ ~~􀀔􀀘􀀗)~~ ~~􀀕 􀀠 􀀔  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCail38g35D5FL6","https://ap.wps.com/l/cbCail38g35D5FL6","pdf",44295,"English","# Identify ellipse features and sketch graphs\n# Compute ellipse measurements\n# Write standard form equations of ellipses","[{\"question\":\"What ellipse elements does the worksheet ask you to identify first?\",\"answer\":\"For each ellipse, it asks for the center, vertices, co-vertices, and foci, and then to sketch the graph based on them.\"},{\"question\":\"Besides vertices and foci, what additional measurements are required?\",\"answer\":\"It requires the length of the major axis, length of the minor axis, length of the latus rectum, and the eccentricity for each ellipse.\"},{\"question\":\"What is the final task after collecting the information?\",\"answer\":\"The worksheet asks you to use the provided information to write the standard form equation of each ellipse.\"}]","Ellipses - Infinite Precalculus Worksheet | PDF",1791427012]