[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267093-105":59,"doc-detail-267093-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","writing-equations-of-circles","Writing Equations of Circles","","Worksheet on writing circle equations from given information, focusing on converting between standard form and expanded forms. Problems provide algebraic expressions and coordinate-based descriptions such as center and radius, endpoints of a diameter, points on the circle, tangency conditions to vertical lines, and translations with specified left/right and up/down shifts. Exercises also include circumference, area, and three-point circle definitions to practice forming accurate circle 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left/right and up/down) is applied to shift the circle’s center before forming the corresponding standard form equation.","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},267093,1789414755,{"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":130,"read_time":52},24189269381491,"https://ap-avatar.wpscdn.com/avatar/160000cf11732dd8392?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788146458752108895","Kuta Software-Infinite Algebra 2 Name   \nWriting Equations of Circles Date  Period   \nUse the information provided to write the standard form equation of each circle.  \n1) 8x + x2 − 2 y = 64 − y 2 2) 137 + 6 y = − y 2 − x 2 − 24x  \n3) x 2 + y 2 + 14x − 12 y + 4 = 0 4) y 2 + 2x + x2 = 24y − 120  \n5) x 2 + 2x + y 2 = 55 + 10 y 6) 8x + 32y + y 2 = −263 − x 2  \n7) Center: (−11, −8) 8) Center: (−6, −15) Radius: 4 Radius: 5  \n9) (x − 16)2 + ( y − 6)2 = 1 10) (x + 5)2 + ( y + 7)2 = 36 Translated 4 left, 2 up Translated 5 left, 4 down  \n11) 12)  \n| |  |  |  y |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| − | 1 |  |  |  | 1 |  | 2 | 3 |  |  | 4 | 5 |  |  | 6 x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −1 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −2 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −3 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −4 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| −5 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n1  \n13) Ends of a diameter: (−17, −9) and (−19, −9) 14) Ends of a diameter: (−3, 11) and (3, −13)  \n15) Center: (−15, 3 7 ) 16) Center: (−11, −14)  \nArea: 2π Area: 16π  \n17) Center: (−5, 12) 18) Center: ( 15, 14)  \nCircumference: 8π Circumference: 2π15  \n19) Center: (2, −5) 20) Center: ( 14, 17)  \nPoint on Circle: (−7, −1) Point on Circle: ( 15, 17)  \n21) Center: (−15, 9) 22) Center: (−2, 12)  \nTangent to x = −17 Tangent to x = −5  \n23) Center lies on the x-axis 24) Center lies in the fourth quadrant Tangent to x = 7 and x = −13 Tangent to x = 7, y = −4, and x = 17  \n25) Three points on the circle: 26) Three points on the circle:(−18, −5), (−7, −16), and (4, −5) (−7, 6), (9, 6), and (−4, 13)  \n27) x 2 + y 2 + 14x + 12 y + 76 = 0 28) x 2 + y 2 − 10x + 20y + 61 = 0 Translated 2 right, 4 down Translated 1 left, 2 down  \n29) x 2 + y 2 + 14x − 8 y + 29 = 0 30) 4 y + y 2 = −28x − x 2 − 191 Translated 3 right, 4 down Translated 4 right  \nKuta Software-Infinite Algebra 2 Name   \nWriting Equations of Circles Date  Period   \nUse the information provided to write the standard form equation of each circle.  \n1) 8x + x2 − 2 y = 64 − y 2  \n(x + 4)2 + ( y − 1)2 = 81  \n3) x 2 + y 2 + 14x − 12 y + 4 = 0  \n(x + 7)2 + ( y − 6)2 = 81  \n5) x 2 + 2x + y 2 = 55 + 10 y  \n(x + 1)2 + ( y − 5)2 = 81  \n7) Center: (−11, −8) Radius: 4  \n(x + 11)2 + ( y + 8)2 = 16  \n9) (x − 16)2 + ( y − 6)2 = 1 Translated 4 left, 2 up  \n(x − 12)2 + ( y − 8)2 = 1  \n11)  \nx 2 + ( y − 3)2 = 9  \n2) 137 + 6 y = − y 2 − x 2 − 24x  \n(x + 12)2 + ( y + 3)2 = 16  \n4) y 2 + 2x + x2 = 24y − 120  \n(x + 1)2 + ( y − 12)2 = 25  \n6) 8x + 32y + y 2 = −263 − x 2  \n(x + 4)2 + ( y + 16)2 = 9  \n8) Center: (−6, −15) Radius: 5  \n(x + 6)2 + ( y + 15)2 = 5  \n10) (x + 5)2 + ( y + 7)2 = 36 Translated 5 left, 4 down  \n(x + 10)2 + ( y + 11)2 = 36  \n12)  \n\n| |  |  |  y |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| − | 1 |  |  |  | 1 |  | 2 | 3 |  |  | 4 | 5 |  |  | 6 x |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −1 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −2 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −3 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | −4 |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| −5 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n1  \n(","cbCaivcvQRmCCnhV","https://ap.wps.com/l/cbCaivcvQRmCCnhV","pdf",41357,"English","# Use the information to write standard form equations\n## Given algebraic forms and circle conditions\n### Center and radius\n### Diameter endpoints and points on the circle\n### Tangent conditions to x = constants\n### Translations of circles\n### Area and circumference","[{\"question\":\"What does the worksheet ask students to do?\",\"answer\":\"Write the standard form equation of each circle using the provided information for every problem.\"},{\"question\":\"What kinds of inputs are used to define each circle?\",\"answer\":\"Circle data include center and radius, diameter endpoints, a point on the circle, tangency to lines like x = k, translations, and geometric measures such as area or circumference.\"},{\"question\":\"How are translations handled in the circle equations?\",\"answer\":\"Each translation instruction (e.g., left/right and up/down) is applied to shift the circle’s center before forming the corresponding standard form equation.\"}]","Writing Equations of Circles | PDF"]