{"id":"cb_question_bank:a5fabb72-e46f-4cb6-b156-6c07140b4863","source_id":"cb_question_bank","source_item_id":"a5fabb72-e46f-4cb6-b156-6c07140b4863","external_id":null,"ibn":"028868-DC","question_id":"856372ca","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane, a circle with radius 5 has center with coordinates negative 8 comma 6 . Which of the following is an equation of the circle?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, a circle with radius 5 has center <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/83354e19a8e2782dfabab6fcfef225c289b68c2a6062af0618b3d2fa2748069e\" alt=\"with coordinates negative 8 comma 6\"></span></span>. Which of the following is an equation of the circle?</p>\n","rationale_html":"<p>Choice B is correct. An equation of a circle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d573a336dc1753ebd43a919d2d966269eabeead14b993a357712d5d7ea39eac9\" alt=\"open parenthesis, x minus h, close parenthesis, squared, plus, open parenthesis, y minus k, close parenthesis, squared, equals r squared\"></span>, where the center of the circle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0fbcdf3067da8003b9a2185c18d77c5f31212a47481a805cefb139af286f21d4\" alt=\"the point with coordinates h comma k \"></span> and the radius is <span class=\"italic\">r</span>. It’s given that the center of this circle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/83354e19a8e2782dfabab6fcfef225c289b68c2a6062af0618b3d2fa2748069e\" alt=\"the point with coordinates negative 8 comma 6 \"></span> and the radius is 5. Substituting these values into the equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c5de1d8dca2917ef0f28b3d22f911e84fe1f7cae55517d182f40045c52607384\" alt=\"open parenthesis, x minus negative 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 5 squared\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a306e736ee951999ab9c2e69b50d90f4642d4999196b3b017ff58e976154a54e\" alt=\"open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 25\"></span>.</p><p>Choice A is incorrect. This is an equation of a circle that has center <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7eed88d406bf7a76f35cffae9b4c9c92cf5bce75139fd7e7e2e3bdf1cc72f0e\" alt=\"8 comma negative 6\"></span>. Choice C is incorrect. This is an equation of a circle that has center <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7eed88d406bf7a76f35cffae9b4c9c92cf5bce75139fd7e7e2e3bdf1cc72f0e\" alt=\"8 comma negative 6\"></span> and radius <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aaaaab78195c53e195e4d77973b5a6313ddaef72fc8548189167ac02255d29ed\" alt=\"the square root of 5\"></span>. Choice D is incorrect. This is an equation of a circle that has radius&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aaaaab78195c53e195e4d77973b5a6313ddaef72fc8548189167ac02255d29ed\" alt=\"the square root of 5\"></span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d2e7b19aa6bd7f19c42c2727838165324fa7b5ed3a66aedafca6b84d8139d4f4\" alt=\"open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 25\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math_expression \">\n                <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a306e736ee951999ab9c2e69b50d90f4642d4999196b3b017ff58e976154a54e\" alt=\"open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 25\"></span></span>\n            </span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math_expression \">\n                <span class=\"math_expression \">\n                  <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5b08e624424e9192feeb6cab0a89b4d790f02dae795968f943f93e1d0919413\" alt=\"open parenthesis, x minus 8, close parenthesis, squared, plus, open parenthesis, y plus 6, close parenthesis, squared, equals 5\"></span></span>\n              </span>\n            </span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math_expression \">\n                <span class=\"math_expression \">\n                  <span class=\"math_expression \">\n                    <span class=\"math_expression \">\n                      <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ec565a95c2a7954ad187ed84a0adb5ddfacb0c2f7178fcbab01b43316d568b0\" alt=\"open parenthesis, x plus 8, close parenthesis, squared, plus, open parenthesis, y minus 6, close parenthesis, squared, equals 5\"></span></span>\n                  </span>\n                </span>\n              </span>\n            </span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}