{"id":"cb_practice_pdf:t7-math-m2-q25","source_id":"cb_practice_pdf","source_item_id":"t7-math-m2-q25","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":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-7","module_number":2,"position":25,"stem":"+14x+y^2 = 6y+109 x^2 In the xy-plane, the graph of the given equation is a circle. What is the length of the circle’s radius? 109","stimulus":"","stimulus_html":null,"stem_html":"<p>+14x+y^2 = 6y+109 x^2 In the xy-plane, the graph of the given equation is a circle. What is the length of the circle’s radius? 109</p>","rationale_html":"<p>Choice C is correct. It’s given that in the xy-plane, the graph of the given equation is a circle. The equation of a circle in the xy-plane can be written - 2+ - 2= 2 in the form ^x hh ^y kh r , where ^h,kh is the center of the circle and r is the length of the circle’s radius. Subtracting 6y from both sides 2+14 + 2=6 +109 2+14 + 2-6 =109 of the equation x x y y yields x x y y . By completing the square, this equation can be rewritten as 2+14 + 14 2 + 2-6 + -6 2 =109+ 14 2 + -6 2 ax x ` 2 j k ay y ` 2 j k ` 2 j ` 2 j . This equation 45 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 2+14 +49 + 2-6 +9 =109+49+9 can be rewritten as ^x x h ^y y h , or +7 2+ -3 2=167 2=167 ^x h ^y h . Therefore, r . Taking the square root of both = 167 =- 167 sides of this equation yields r and r . Since r is the length of the circle’s radius, r must be positive. Therefore, the length of the circle’s 167 radius is . Choice A is incorrect and may result from conceptual or calculation errors. Choice B 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":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>149</p>","ord":0},{"label":"B","content_html":"<p>167</p>","ord":1},{"label":"C","content_html":"<p>341</p>","ord":2},{"label":"D","content_html":"","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}}