[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-523541-105":3,"detail-sidebar-cat-0-en-105":73,"doc-detail-523541-en":122},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":66,"head_meta":68,"extra_data":70,"updated_unix":72},105,"en","kuta-software-infinite-precalculus-polar-forms-of-conic-sections-worksheet","Kuta Software - Infinite Precalculus Polar Forms of Conic Sections - Worksheet","","Kuta Software - Infinite Precalculus worksheet focuses on polar equations of conic sections with a focus at the origin. Problems ask students to compute eccentricity, determine the directrix equation tied to the given focus, and classify each conic as ellipse, parabola, or hyperbola. Additional tasks require writing each polar equation in standard form and, for selected items, graphing the resulting polar conic. A critical thinking question evaluates whether a polar form can represent a circle.",{"@graph":14,"@context":65},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/kuta-software-infinite-precalculus-polar-forms-of-conic-sections-worksheet/523541/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/kuta-software-infinite-precalculus-polar-forms-of-conic-sections-worksheet/523541.png","ImageObject",300,407,{"name":42,"@type":43},"hdkawk","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59],{"name":60,"@type":61,"acceptedAnswer":62},"Can the worksheet’s polar form be used to represent a circle? 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With eccentricity 0, the polar form simplifies to r being a constant that represents a single point, so it does not produce a true circle in this form.","Answer","https://schema.org",{"og:url":32,"og:type":67,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":69,"canonical":32},"index,follow",{"doc_id":71,"site_id":7},523541,1791513370,{"code":4,"msg":74,"data":75},"success",[76,80,84,87,92,97,102,107,111,114,118],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":81,"show_sort_weight":82,"slug":83},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":85,"slug":86},70,"exam",{"id":88,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},5,"Comic",60,"comic",{"id":93,"doc_module":4,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},6,"Technology",50,"technology",{"id":98,"doc_module":4,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},7,"Healthcare",40,"healthcare",{"id":103,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},"Religion & Spirituality",20,"religion-spirituality",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":109,"slug":113},"World Cup","world-cup",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":115,"slug":117},10,"Lifestyle","lifestyle",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":88,"slug":121},19,"General","general",{"code":4,"msg":74,"data":123},{"doc_id":71,"user_id":124,"nickname":42,"user_avatar":125,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":131,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":12,"update_tm":135,"read_time":115,"preview_page_count":4},3985747859855,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Polar Forms of Conic Sections  \nName  Date  Period   \nEach polar equation describes a conic section with a focus at the origin. Find the eccentricity, find the equation of the directrix associated with the focus at the origin, and classify the conic section.  \n1) r 􀀠 ~~ ~~􀀔~~ ~~􀀐~~ ~~􀀓􀀓􀀑~~ ~~􀀑􀀛􀀛sin~~ ~~􀁔~~ ~~ 2) r 􀀠 ~~ ~~􀀔~~ ~~􀀐~~ ~~os~~ ~~􀁔  \n3) r 􀀠 ~~ ~~􀀔~~ ~~􀀎~~ ~~􀀕~~ ~~􀁔~~ ~~ 4) r 􀀠 􀀕~~ ~~􀀐~~ ~~􀀔􀀕􀀓sin~~ ~~􀁔  \n5) r 􀀠 􀀗~~ ~~􀀐~~ ~~􀀔􀀑􀀛􀀙sin~~ ~~􀁔~~ ~~ 6) r 􀀠 􀀕~~ ~~􀀐~~ ~~􀀔􀀗~~ ~~􀀑􀀗􀀛􀀑os~~ ~~􀁔  \nEach problem describes a conic section with a focus at the origin. Classify the conic section, and write the polar equation in standard form.  \n7) Eccentricity: 􀀔 8) Eccentricity: 􀀔􀀑􀀘  \nDirectrix for focus at origin: y 􀀠 􀀐􀀙 Directrix for focus at origin: x 􀀠 􀀕  \n9) Eccentricity: 􀀕􀀑􀀔 10) Eccentricity: 􀀓􀀑􀀘  \nDirectrix for focus at origin: y 􀀠 􀀐􀀖 Directrix for focus at origin: y 􀀠 􀀐􀀕  \nEach problem describes a conic section with a focus at the origin. Find the equation of the directrix associated with the focus at the origin, classify the conic section, and write the polar equation in standard form.  \n11) EccentVertice:cty􀀓,:~~ ~~􀀓􀀗􀀖􀀘, (􀀓 , 􀀐􀀗)  \n12) Eccentricity: 􀀔 Vertex: (􀀐􀀔 , 􀀓)  \nEach polar equation describes a conic section with a focus at the origin. Find the eccentricity, find the equation of the directrix associated with the focus at the origin, classify the conic section, and graph the polar equation.  \n13) r 􀀠  􀀔􀀜􀀑􀀛   \n􀀖 􀀎 􀀙􀀑􀀙 cos 􀁔􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \n14) r 􀀠  􀀜􀀑􀀙   \n􀀗 􀀎 􀀔􀀑􀀙 cos 􀁔􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nCritical thinking question:  \n15) Is it possible to use r 􀀠 ~~ ~~􀀔~~ ~~􀀎~~ ~~edecos~~ ~~􀁔 to represent a circle? Explain your answer.  \nKuta Software-Infinite Precalculus Polar Forms of Conic Sections  \nName  Date  Period   \nEach polar equation describes a conic section with a focus at the origin. Find the eccentricity, find the equation of the directrix associated with the focus at the origin, and classify the conic section.  \n1) r 􀀠  􀀓􀀑􀀛   \n􀀔 􀀐 􀀓􀀑􀀛sin 􀁔  \nEccentricity: 􀀓􀀑􀀛  \nDirectrix: y 􀀠 􀀐􀀔 Ellipse  \n3) r 􀀠 ~~ ~~􀀔~~ ~~􀀎~~ ~~􀀕~~ ~~􀁔  \nEccentricity: 􀀕  \nDirectrix: x 􀀠 􀀔 Hyperbola  \n5) r 􀀠 􀀗~~ ~~􀀐~~ ~~􀀔􀀑􀀛􀀙sin~~ ~~􀁔  \nEccentricity: 􀀓􀀑􀀗  \nDirectrix: y 􀀠 􀀐􀀘 Ellipse  \n2) r 􀀠 ~~ ~~􀀔~~ ~~􀀐~~ ~~os~~ ~~􀁔  \nEccentricity: 􀀔  \nDirectrix: x 􀀠 􀀐􀀔 Parabola  \n4) r 􀀠 􀀕~~ ~~􀀐~~ ~~􀀔􀀕􀀓sin~~ ~~􀁔  \nEccentricity: 􀀔  \nDirectrix: y 􀀠 􀀐􀀘 Parabola  \n6) r 􀀠  􀀔􀀗􀀑􀀗   \n􀀕 􀀐 􀀗􀀑􀀛 cos 􀁔  \nEccentricity: 􀀕􀀑􀀗  \nDirectrix: x 􀀠 􀀐􀀖 Hyperbola  \nEach problem describes a conic section with a focus at the origin. Classify the conic section, and write the polar equation in standard form.  \n7) Eccentricity: 􀀔  \nDirectrix for focus at origin: y 􀀠 􀀐􀀙  \nParabola  \n􀀙 r 􀀠  􀀔 􀀐 sin 􀁔  \n9) Eccentricity: 􀀕􀀑􀀔  \nDirectrix for focus at origin: y 􀀠 􀀐􀀖  \nHyperbola  \n􀀙􀀑􀀖 r 􀀠  􀀔 􀀐 􀀕􀀑􀀔sin 􀁔  \n8) Eccentricity: 􀀔􀀑􀀘  \nDirectrix for focus at origin: x 􀀠 􀀕  \nHyperbola  \n􀀖 r 􀀠  􀀔 􀀎 􀀔􀀑􀀘 cos 􀁔  \n10) Eccentricity: 􀀓􀀑􀀘  \nDirectrix for focus at origin: y 􀀠 􀀐􀀕  \nEllipse  \n􀀔 r 􀀠  􀀔 􀀐 􀀓􀀑􀀘sin 􀁔  \nEach problem describes a conic section with a focus at the origin. Find the equation of the directrix associated with the focus at the origin, classify the conic section, and write the polar equation in standard form.  \n11) EccentVertice:cty􀀓,:~~ ~~􀀓􀀗􀀖􀀘, (􀀓 , 􀀐􀀗)  \nDirectrix: y 􀀠 􀀗 Ellipse  \n 􀀕  r 􀀠 􀀔 􀀎 􀀓􀀑􀀘sin 􀁔  \n12) Eccentricity: 􀀔  \nVertex: (􀀐􀀔 , 􀀓)  \nDirectrix: x 􀀠 􀀐􀀕 Parabola  \n􀀕 r 􀀠  􀀔 􀀐 cos 􀁔  \nEach polar equation describes a conic section with a focus at the origin. Find the eccentricity, find the equation of the directrix associated with the focus at the origin, classify the conic section, and graph the polar equation.  \n13) r 􀀠  􀀔􀀜􀀑􀀛   \n􀀖 􀀎 􀀙􀀑􀀙 cos 􀁔􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nEccentricity: 􀀕􀀑􀀕  \nDirectrix: x 􀀠 􀀖 Hyperbola  \n14) r 􀀠  􀀜􀀑􀀙   \n􀀗 􀀎 􀀔􀀑􀀙 cos 􀁔􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nEccentricity: 􀀓􀀑􀀗  \nDirectrix: x 􀀠 􀀙 Ellipse  \nCritical thinking question:  \n15) Is it possible to use r 􀀠 ~~ ~~􀀔~~ ~~􀀎~~ ~~edecos~~ ~~􀁔 to represent a circle? Explain your answer.  \nNo. Circles have an eccentricity of 0. This sim","cbCaisB1s7VlNRV4","https://ap.wps.com/l/cbCaisB1s7VlNRV4","pdf",39246,"English","# Determine eccentricity and directrix\n## Classify the conic and write polar equations in standard form\n## Vertex and graphing tasks\n# Critical thinking question","[{\"question\":\"Can the worksheet’s polar form be used to represent a circle? Why or why not?\",\"answer\":\"A circle has eccentricity 0. With eccentricity 0, the polar form simplifies to r being a constant that represents a single point, so it does not produce a true circle in this form.\"}]","Kuta Software - Infinite Precalculus Polar Forms of Conic Sections - Worksheet | PDF",1791426978]