{"id":"cb_practice_pdf:t10-math-m1-q23","source_id":"cb_practice_pdf","source_item_id":"t10-math-m1-q23","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-10","module_number":1,"position":23,"stem":"Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point? (x−8)^2 +(y−8)^2 = 16","stimulus":"","stimulus_html":null,"stem_html":"<p>Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point? (x−8)^2 +(y−8)^2 = 16</p>","rationale_html":"<p>- 2+ - 2= 2 Choice C is correct. The graph of the equation ^x hh ^y kh r in the xy-plane is a circle with center ^h,kh and a radius of length r. The radius of a circle is the distance from the center of the circle to any point on the circle. If a circle in the xy-plane intersects the y-axis at exactly one point, then the perpendicular distance from the center of the circle to this point on the y-axis must be equal to the length of the circle’s radius. It follows that the x-coordinate of the circle’s center must be equivalent to the length of the circle’s radius. In other words, if the - 2+ - 2= 2 graph of ^x hh ^y kh r is a circle that intersects the y-axis at exactly one = -4 2+ -9 2=16 point, then r h must be true. The equation in choice C is ^x h ^y h , -4 2+ -9 2=42 - 2+ - 2= 2 or ^x h ^y h . This equation is in the form ^x hh ^y kh r , where = = = 4,9 h 4, k 9, and r 4, and represents a circle in the xy-plane with center ^ h = and radius of length 4. Substituting 4 for r and 4 for h in the equation r h = = yields 4 4 , or 4 4, which is true. Therefore, the equation in choice C represents a circle in the xy-plane that intersects the y-axis at exactly one point. Choice A is incorrect. This is the equation of a circle that does not intersect the y-axis at any point. Choice B is incorrect. This is an equation of a circle that intersects the x-axis, not the y-axis, at exactly one point. Choice D is incorrect. This is the equation of a circle with the center located on the y-axis and thus intersects the y-axis at exactly two points, not exactly one point.</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>(x−8)^2 +(y−4)^2 = 16</p>","ord":0},{"label":"B","content_html":"","ord":1},{"label":"C","content_html":"<p>(x−4)^2 +(y−9)^2 = 16</p>","ord":2},{"label":"D","content_html":"<p>x^2 +(y−9)^2 = 16</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}}