{"id":"cb_practice_pdf:t4-math-m2-q25","source_id":"cb_practice_pdf","source_item_id":"t4-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-4","module_number":2,"position":25,"stem":"The equation x^2 +( y −1)^2 = 49 represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equations represents circle B? ( −2)^2 +( −1)^2 = 49","stimulus":"","stimulus_html":null,"stem_html":"<p>The equation x^2 +( y −1)^2 = 49 represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equations represents circle B? ( −2)^2 +( −1)^2 = 49</p>","rationale_html":"<p>Choice D is correct. The graph in the xy-plane of an equation of the form ( - )2+( - )2= 2 ( ) x h y k r is a circle with center h, k and a radius of length r. It’s 2+( - )2= given that circle A is represented by x y 1 49, which can be rewritten as 2+( - )2= 2 ( ) x y 1 7 . Therefore, circle A has center 0, 1 and a radius of length 7. Shifting circle A down two units is a rigid vertical translation of circle A that does not change its size or shape. Since circle B is obtained by shifting circle A down two units, it follows that circle B has the same radius as circle A, and for each point ( ) ( - ) ( ) x, y on circle A, the point x, y 2 lies on circle B. Moreover, if h, k is the ( - ) center of circle A, then h, k 2 is the center of circle B. Therefore, circle B has a ( - ) ( - ) radius of 7 and the center of circle B is 0, 1 2 , or 0, 1. Thus, circle B can be 2+( + )2= 2 2+( + )2= represented by the equation x y 1 7 , or x y 1 49. Choice A is incorrect. This is the equation of a circle obtained by shifting circle A right 2 units. Choice B is incorrect. This is the equation of a circle obtained by shifting circle A up 2 units. Choice C is incorrect. This is the equation of a circle obtained by shifting circle A left 2 units.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>x y</p>","ord":0},{"label":"B","content_html":"<p>x^2 +( y −3)^2 = 49</p>","ord":1},{"label":"C","content_html":"<p>( x +2)^2 +( y −1)^2 = 49</p>","ord":2},{"label":"D","content_html":"<p>x^2 +( y +1)^2 = 49 STO</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}}