{"id":"cb_practice_pdf:t7-math-m1-q15","source_id":"cb_practice_pdf","source_item_id":"t7-math-m1-q15","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":1,"position":15,"stem":"A circle in the xy-plane has the equation x−13 + y−k = 64 ()^2 ()^2. Which of the following gives the center of the circle and its radius? (13,k)","stimulus":"","stimulus_html":null,"stem_html":"<p>A circle in the xy-plane has the equation x−13 + y−k = 64 ()^2 ()^2. Which of the following gives the center of the circle and its radius? (13,k)</p>","rationale_html":"<p>Choice A is correct. For a circle in the xy-plane that has the equation - 2+ - 2= 2 ^x hh ^y kh r , where h, k, and r are constants, ^h,kh is the center of the circle and the positive value of r is the radius of the circle. In the given equation, =13 2=64 2=64 =! h and r . Taking the square root of each side of r yields r 8. 13, Therefore, the center of the circle is at ^ kh and the radius is 8. Choice B is incorrect. This gives the center and radius of a circle with equation - 2+ -13 2=64 -13 2+ - 2=64 ^x kh ^y h , not ^x h ^y kh . Choice C is incorrect. This - 2+ -13 2=4,096 gives the center and radius of a circle with equation ^x kh ^y h , -13 2+ - 2=64 not ^x h ^y kh . Choice D is incorrect. This gives the center and -13 2+ - 2=4,096 radius of a circle with equation ^x h ^y kh , not -13 2+ - 2=64 ^x h ^y kh . 34 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>The center is at and the radius is 8. (k,13)</p>","ord":0},{"label":"B","content_html":"<p>The center is at and the radius is 8. (k,13)</p>","ord":1},{"label":"C","content_html":"<p>The center is at and the radius is 64. (13,k)</p>","ord":2},{"label":"D","content_html":"<p>The center is at and the radius is 64.</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}}