[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523556-105":59,"doc-detail-523556-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","hyperbolas-identify-and-sketch","Hyperbolas - Identify and Sketch","","Worksheets for identifying key features of hyperbolas in coordinate form, including vertices, foci, and asymptotes, followed by sketching each graph. Additional problems request extended properties such as direction of opening, lengths of the transverse and conjugate axes, latus rectum length, and eccentricity. A final section uses given points to write standard-form equations for hyperbolas, emphasizing correct parameter extraction and consistent graphing.",{"@graph":69,"@context":122},[70,84,105],{"@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/hyperbolas-identify-and-sketch/523556/",{"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/hyperbolas-identify-and-sketch/523556.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":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What must be identified for each hyperbola before graphing?","Question",{"text":112,"@type":113},"Vertices, foci, and asymptotes are identified first, and then each graph is sketched.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which additional hyperbola measurements are required in the extended section?",{"text":117,"@type":113},"Direction of opening, length of the transverse axis, length of the conjugate axis, length of the latus rectum, and eccentricity.",{"name":119,"@type":110,"acceptedAnswer":120},"How do the equation-writing problems work?",{"text":121,"@type":113},"Given information such as vertices or center-related details is used to write each hyperbola in standard form.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523556,1791732368,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},962090894170,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Precalculus Name   \nHyperbolas Date  Period   \nIdentify the vertices, foci, and asymptotes of each. Then sketch the graph.  \n1) x~~ ~~􀀕􀀜 􀀐 y􀀕􀀕􀀘~~ ~~ 􀀠 􀀔  \n3) y􀀔􀀕􀀙 􀀐 (x 􀀎 􀀗)􀀕 􀀠 􀀔  \n5) 􀀜x 􀀕 􀀐 􀀗y 􀀕 􀀐 􀀔􀀛 x 􀀎 􀀔􀀙y 􀀐 􀀗􀀖 􀀠 􀀓  \n2) (y 􀀎 􀀗)􀀕 􀀐 (x 􀀐 􀀖)􀀕 􀀠 􀀔  \n4) y􀀔􀀕􀀓 􀀐 (x~~ ~~􀀔)􀀕 􀀠 􀀔  \n6) 􀀐􀀜x 􀀕 􀀐 􀀖􀀕 y 􀀠 􀀐􀀔􀀙y 􀀕 􀀎 􀀔􀀕􀀛  \nIdentify the vertices, foci, asymptotes, direction of opening, length of the transverse axis, length of the conjugate axis, length of the latus rectum, and eccentricity of each.  \n7) x 􀀕 􀀐 y 􀀕 􀀐 􀀙x 􀀎 􀀔􀀙y 􀀐 􀀔􀀔􀀜 􀀠 􀀓 8) 􀀐􀀗x 􀀕 􀀎 y 􀀕 􀀎 􀀛 x 􀀐 􀀕􀀓y 􀀐 􀀗 􀀠 􀀓  \nUse the information provided to write the standard form equation of each hyperbola.  \n9) Vertices: (􀀔 􀀎 􀀖 􀀔􀀘 , 􀀐􀀚), (􀀔 􀀐 􀀖 􀀔􀀘 , 􀀐􀀚 )  \nEndpoints of Conjugate Axis: (􀀔 , 􀀐􀀚 􀀎 􀀘 􀀘 )  \n(􀀔 , 􀀐􀀚 􀀐 􀀘 􀀘 )  \n11) Vertices: (􀀐􀀔􀀓 , 􀀔), (􀀐􀀔􀀓 , 􀀐􀀔􀀚) Perimeter of Central Rectangle = 􀀚􀀙  \n13) Center at (􀀔􀀓 , 􀀐􀀗)  \nTransverse axis is vertical and 􀀔􀀛 units long Conjugate axis is 􀀔􀀓 units long  \n15)  \n10) Vertices: (􀀔􀀜 , 􀀕), (􀀔 , 􀀕)  \nFoci: (􀀔􀀓 􀀎 􀀔􀀖􀀓 , 􀀕), (􀀔􀀓 􀀐 􀀔􀀖􀀓 , 􀀕)  \n12) Vertices: (􀀚 , 􀀐􀀕), (􀀘 , 􀀐􀀕)  \nAsymptotes: y 􀀠 􀀔􀀔 x 􀀐 􀀙􀀛 y 􀀠 􀀐􀀔􀀔 x 􀀎 􀀙􀀗  \n14) Foci: (􀀙 , 􀀔 􀀎 􀀕 􀀘􀀛 ), (􀀙 , 􀀔 􀀐 􀀕 􀀘􀀛 ) Points on the hyperbola are 􀀕􀀛 units closer to one focus than the other  \n16) Center at (􀀐􀀙 , 􀀜) Vertex at (􀀐􀀔􀀛 , 􀀜) Eccentricity = 􀀘􀀗  \nKuta Software-Infinite Precalculus Name   \nHyperbolas Date  Period   \nIdentify the vertices, foci, and asymptotes of each. Then sketch the graph.  \n1) x~~ ~~􀀕􀀜 􀀐 y􀀕􀀕􀀘~~ ~~ 􀀠 􀀔  \n3) y􀀔􀀕􀀙 􀀐 (x 􀀎 􀀗)􀀕 􀀠 􀀔  \n5) 􀀜x 􀀕 􀀐 􀀗y 􀀕 􀀐 􀀔􀀛 x 􀀎 􀀔􀀙y 􀀐 􀀗􀀖 􀀠 􀀓  \n2) (y 􀀎 􀀗)􀀕 􀀐 (x 􀀐 􀀖)􀀕 􀀠 􀀔  \n4) y􀀔􀀕􀀓 􀀐 (x~~ ~~􀀔)􀀕 􀀠 􀀔  \n6) 􀀐􀀜x 􀀕 􀀐 􀀖􀀕 y 􀀠 􀀐􀀔􀀙y 􀀕 􀀎 􀀔􀀕􀀛  \nIdentify the vertices, foci, asymptotes, direction of opening, length of the transverse axis, length of the conjugate axis, length of the latus rectum, and eccentricity of each.  \n7) x 􀀕 􀀐 y 􀀕 􀀐 􀀙x 􀀎 􀀔􀀙y 􀀐 􀀔􀀔􀀜 􀀠 􀀓  \nVertices: (􀀔􀀔 , 􀀛), (􀀐􀀘 , 􀀛)  \nFoci: (􀀖 􀀎 􀀛 􀀕 , 􀀛), (􀀖 􀀐 􀀛 􀀕 , 􀀛)  \nAsym.: y 􀀠 x 􀀎 􀀘  \ny 􀀠 􀀐x 􀀎 􀀔􀀔 Opens left/right Transverse Axis: 􀀔􀀙 units  \nConjugate Axis: 􀀔􀀙 units  \nLatus Rectum: 􀀔􀀙 units  \nEccentricity: 􀀕 􀁼 􀀔􀀑􀀗􀀔􀀗  \n8) 􀀐􀀗x 􀀕 􀀎 y 􀀕 􀀎 􀀛 x 􀀐 􀀕􀀓y 􀀐 􀀗 􀀠 􀀓  \nVertices: (􀀔 , 􀀕􀀓), (􀀔 , 􀀓)  \nFoci: (􀀔 , 􀀔􀀓 􀀎 􀀘 􀀘 ), (􀀔 , 􀀔􀀓 􀀐 􀀘 􀀘 )  \nAsym.: y 􀀠 􀀕x 􀀎 􀀛  \ny 􀀠 􀀐􀀕x 􀀎 􀀔􀀕 Opens up/down Transverse Axis: 􀀕􀀓 units  \nConjugate Axis: 􀀔􀀓 units  \nLatus Rectum: 􀀘 units  \nEccentricity: ~~ ~~􀀕~~ ~~ 􀁼 􀀔􀀑􀀔􀀔􀀛  \nUse the information provided to write the standard form equation of each hyperbola.  \n9) Vertices: (􀀔 􀀎 􀀖 􀀔􀀘 , 􀀐􀀚), (􀀔 􀀐 􀀖 􀀔􀀘 , 􀀐􀀚 )  \nEndpoints of Conjugate Axis: (􀀔 , 􀀐􀀚 􀀎 􀀘 􀀘 )  \n(􀀔 , 􀀐􀀚 􀀐 􀀘 􀀘 )  \n~~ ~~(x~~ ~~~~ ~~􀀔􀀘~~ ~~)~~ ~~􀀕 􀀐 (y~~ ~~􀀔~~ ~~􀀚􀀘)~~ ~~􀀕 􀀠 􀀔  \n11) Vertices: (􀀐􀀔􀀓 , 􀀔), (􀀐􀀔􀀓 , 􀀐􀀔􀀚) Perimeter of Central Rectangle = 􀀚􀀙  \n~~ ~~(y~~ ~~􀀔􀀛)􀀕 􀀐 (x~~ ~~􀀔􀀓􀀓)􀀕 􀀠 􀀔  \n13) Center at (􀀔􀀓 , 􀀐􀀗)  \nTransverse axis is vertical and 􀀔􀀛 units long Conjugate axis is 􀀔􀀓 units long  \n~~ ~~(y~~ ~~􀀔􀀗)􀀕 􀀐 (x~~ ~~~~ ~~􀀔􀀘~~ ~~􀀓)􀀕 􀀠 􀀔  \n10) Vertices: (􀀔􀀜 , 􀀕), (􀀔 , 􀀕)  \nFoci: (􀀔􀀓 􀀎 􀀔􀀖􀀓 , 􀀕), (􀀔􀀓 􀀐 􀀔􀀖􀀓 , 􀀕)  \n~~ ~~(x~~ ~~~~ ~~􀀔􀀔~~ ~~􀀓)􀀕 􀀐 (y~~ ~~􀀜􀀕)􀀕 􀀠 􀀔  \n12) Vertices: (􀀚 , 􀀐􀀕), (􀀘 , 􀀐􀀕)  \nAsymptotes: y 􀀠 􀀔􀀔 x 􀀐 􀀙􀀛 y 􀀠 􀀐􀀔􀀔 x 􀀎 􀀙􀀗  \n(x 􀀐 􀀙)􀀕 􀀐 (y~~ ~~􀀔~~ ~~􀀕􀀔)~~ ~~􀀕 􀀠 􀀔  \n14) Foci: (􀀙 , 􀀔 􀀎 􀀕 􀀘􀀛 ), (􀀙 , 􀀔 􀀐 􀀕 􀀘􀀛 ) Points on the hyperbola are 􀀕􀀛 units closer to one focus than the other  \n~~ ~~(y~~ ~~􀀔􀀔􀀙~~ ~~)~~ ~~􀀕 􀀐 (x~~ ~~􀀙􀀙)􀀕 􀀠 􀀔  \n15)  \n􀀕  \nx  \n􀀕􀀘  \n􀀐  \n􀀕  \ny   \n􀀗  \n􀀠 􀀔 16) Center at (􀀐􀀙 , 􀀜)  \nVertex at (􀀐􀀔􀀛 , 􀀜) Eccentricity = 􀀘􀀗  (x 􀀎 􀀙)􀀕   (y 􀀐 􀀜)􀀕   \n􀀐􀀔􀀗􀀗 􀀛􀀔  \n􀀠 􀀔  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCailocGDTQYIXA","https://ap.wps.com/l/cbCailocGDTQYIXA","pdf",75348,"English","# Identify vertices, foci, and asymptotes - then sketch\n# Compute additional hyperbola features\n## Standard-form equations from given information","[{\"question\":\"What must be identified for each hyperbola before graphing?\",\"answer\":\"Vertices, foci, and asymptotes are identified first, and then each graph is sketched.\"},{\"question\":\"Which additional hyperbola measurements are required in the extended section?\",\"answer\":\"Direction of opening, length of the transverse axis, length of the conjugate axis, length of the latus rectum, and eccentricity.\"},{\"question\":\"How do the equation-writing problems work?\",\"answer\":\"Given information such as vertices or center-related details is used to write each hyperbola in standard form.\"}]","Hyperbolas - Identify and Sketch | PDF",1791427010]