{"id":"cb_practice_pdf:t5-math-m1-q22","source_id":"cb_practice_pdf","source_item_id":"t5-math-m1-q22","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-5","module_number":1,"position":22,"stem":"(x+4)^2 +(y−19)^2 = 121 The graph of the given equation is a circle in the xy-plane. The point (a,b) lies on the circle. Which of the following is a possible value for a?","stimulus":"","stimulus_html":null,"stem_html":"<p>(x+4)^2 +(y−19)^2 = 121 The graph of the given equation is a circle in the xy-plane. The point (a,b) lies on the circle. Which of the following is a possible value for a?</p>","rationale_html":"<p>- 2+ - 2= 2 Choice B is correct. An equation of the form ^x hh ^y kh r , where h, k, and r are constants, represents a circle in the xy-plane with center ^h,kh and radius r. Therefore, the circle represented by the given equation has center -4,19 - ^ h and radius 11. Since the center of the circle has an x-coordinate of 4 and the radius of the circle is 11, the least possible x-coordinate for any point on -4-11 -15 the circle is , or . Similarly, the greatest possible x-coordinate for any -4+11 point on the circle is , or 7. Therefore, if the point ^a,bh lies on the circle, it -15# #7 -14 must be true that a . Of the given choices, only satisfies this inequality. 39 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>−16 −14</p>","ord":0},{"label":"B","content_html":"<p>11</p>","ord":1},{"label":"C","content_html":"","ord":2},{"label":"D","content_html":"<p>19</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}