[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-267090-en":59,"doc-seo-267090-105":81},{"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":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":73,"language":74,"language_code":75,"site_id":76,"html_lang":75,"table_of_contents":77,"faqs":78,"seo_title":79,"seo_description":66,"update_tm":80,"read_time":39},267090,962085662650,"Dozel","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","SAT “Equation of a Circle” Practice Problems Worksheet - Circle Center and Radius Questions","SAT “Equation of a Circle” practice problems worksheet focused on writing and interpreting circle equations in standard form. It covers identifying circle center and radius from given (x−h)^2+(y−k)^2=r^2 equations, generating the equation when a center and radius are provided, and converting expanded forms to reveal the radius or the center using completing-the-square. Includes 8 multiple-choice items with an answer key for self-checking.","SAT “Equation of a Circle” Practice Problems Worksheet  \nOver the past few years, the College Board has transitioned from practically never asking about the equation for graphing a circle to now asking it on just about every test (I would say “every test,” but there is always that possibility it may not be on one test as a rare exception) . For reference, here’s the equation for graphing a circle:  \nFor a circle with center (h, k),(􀝔 − ℎ)2 + (􀝕 − 􀝇)2 = 􀜴􀜽􀝀􀝅􀝑􀝏2  \nThe good news is that the questions they use to test your knowledge of this concept are not varied; in fact, there are only three ways I have seen them actually test this concept, and the three question types are seen in questions 1-3 (here’s the equation, now identify the center and radius), 4-5 (here’s the center and radius, now identify the equation), and 6-8 (reformat the given equation to look like the equation for graphing a circle by completing the square, then identify the center or radius) . If you can do these problems, then you’re good for this question type.  \n1. (􀝔 − 8)2 + (􀝕 − 6)2 = 36  \nFor the equation above, what is the coordinate point for the center of the circle as well as the circle’s radius?  \nA) Center: (-8, -6), Radius: 36  \nB) Center: (8, 6), Radius: 36  \nC) Center: (-8, -6), Radius: 6  \nD) Center: (8, 6), Radius: 6  \n2. (􀝔 + 14)2 + (􀝕 + 2)2 = 64  \nFor the equation above, what is the coordinate point for the center of the circle as well as the circle’s radius?  \nA) Center: (14, 2), Radius: 8  \nB) Center: (14, 2), Radius: 64  \nC) Center: (-14, -2), Radius: 8  \nD) Center: (-14, -2), Radius: 64  \n3. (􀝔 − 11)2 + (􀝕 + 4)2 = 49  \nFor the equation above, what is the coordinate point for the center of the circle as well as the circle’s radius?  \nA) Center: (11, -4), Radius: 7  \nB) Center: (11, -4), Radius: 49  \nC) Center: (-11, 4), Radius: 49  \nD) Center: (-11, 4), Radius: 7  \n4. Find the equation of a circle with center (12, -3) and a radius of 3:  \nA) (􀝔 − 12)2 + (􀝕 + 3)2 = 3  \nB) (􀝔 − 12)2 + (􀝕 + 3)2 = 9  \nC) (􀝔 + 12)2 + (􀝕 − 3)2 = 3  \nD) (􀝔 + 12)2 + (􀝕 − 3)2 = 9  \n5. Find the equation of a circle with center (-7, 11) and a radius of 9:  \nA) (􀝔 + 7)2 + (􀝕 − 11)2 = 81  \nB) (􀝔 + 7)2 + (􀝕 + 11)2 = 9  \nC) (􀝔 − 7)2 + (􀝕 − 11)2 = 81  \nD) (􀝔 − 7)2 + (􀝕 + 11)2 = 9  \n􀝔 2 + 10x + 􀝕2 – 6y = -18  \n6. The graph of the equation shown above is a circle. What is the radius of the circle?  \nA) 3  \nB) 4  \nC) 5  \nD) 9  \n􀝔 2 + 18x + 􀝕2 – 8y = -48  \n7. The graph of the equation shown above is a circle. What is the radius of the circle?  \nA) 4  \nB) 5  \nC) 6  \nD) 7  \n􀝔 2-4x + 􀝕2 +6y = 87  \n8. The graph of the equation shown above is a circle. What is the coordinate point of the center of the circle?  \nA) (13, 10)  \nB) (4, 13)  \nC) (-4, 6)  \nD) (2, -3)  \nAnswer Key:  \n1. D  \n2. C  \n3. A  \n4. B  \n5. A  \n6. B  \n7. D  \n8. D","cbCail3ndhdi4UnL","https://ap.wps.com/l/cbCail3ndhdi4UnL","pdf",154447,21,3,"English","en",105,"# Practice Problems\n## Center and Radius from Standard Form\n## Equation from Center and Radius\n## Radius or Center from Expanded Form\n# Answer Key","[{\"question\":\"How do you find the center and radius from a standard circle equation on the worksheet?\",\"answer\":\"Use the form (x−h)^2+(y−k)^2=r^2. The center is (h,k) and the radius is r.\"},{\"question\":\"What method is used for questions that give an expanded equation and ask for radius or center?\",\"answer\":\"Convert the expanded equation to standard form by completing the square, then read the radius (r) and center (h,k).\"},{\"question\":\"What topics are covered across questions 1–8 in this practice set?\",\"answer\":\"Questions 1–3 identify center and radius from standard form, 4–5 write an equation from a given center and radius, and 6–8 use completing-the-square to determine the radius or the center from expanded equations.\"}]","SAT “Equation of a Circle” Practice Problems Worksheet - Circle Center and Radius Questions | PDF",1789414708,{"code":4,"msg":82,"data":83},"ok",{"site_id":76,"language":75,"slug":84,"title":65,"keywords":85,"description":66,"schema_data":86,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":80},"sat-equation-of-a-circle-practice-problems-worksheet-circle-center-and-radius-questions","",{"@graph":87,"@context":138},[88,101,121],{"@type":89,"itemListElement":90},"BreadcrumbList",[91,95,97,99],{"item":92,"name":93,"@type":94,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":96,"name":9,"@type":94,"position":14},"https://docshare.wps.com/document/",{"item":98,"name":20,"@type":94,"position":73},"https://docshare.wps.com/document/exam/",{"item":100,"name":65,"@type":94,"position":19},"https://docshare.wps.com/document/sat-equation-of-a-circle-practice-problems-worksheet-circle-center-and-radius-questions/267090/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":75,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/sat-equation-of-a-circle-practice-problems-worksheet-circle-center-and-radius-questions/267090.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":92,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-10-28","2026-09-14",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"How do you find the center and radius from a standard circle equation on the worksheet?","Question",{"text":128,"@type":129},"Use the form (x−h)^2+(y−k)^2=r^2. The center is (h,k) and the radius is r.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"What method is used for questions that give an expanded equation and ask for radius or center?",{"text":133,"@type":129},"Convert the expanded equation to standard form by completing the square, then read the radius (r) and center (h,k).",{"name":135,"@type":126,"acceptedAnswer":136},"What topics are covered across questions 1–8 in this practice set?",{"text":137,"@type":129},"Questions 1–3 identify center and radius from standard form, 4–5 write an equation from a given center and radius, and 6–8 use completing-the-square to determine the radius or the center from expanded equations.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":76}]