20 Circle A in the xy-plane has the equation x + 5 + y - 5 = 25. Circle B has the same ^ h^2 ^ h^2 center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is x + 5 + y - 5 = k, where k ^ h^2 ^ h^2 is a constant. What is the value of k?
Correct answer: 100 (parsed from the explanation — this source omits an answer key for this item)
Explanation
100 The correct answer is . An equation of a circle in the xy-plane can be written - 2+ - 2= 2 as ^x th ^y uh r , where the center of the circle is ^t,uh, the radius of the circle is r, and where t, u, and r are constants. It’s given that the equation of +5 2+ -5 2=25 +5 2+ -5 2=52 circle A is ^x h ^y h , which is equivalent to ^x h ^y h . -5,5 Therefore, the center of circle A is ^ h and the radius of circle A is 5. It’s given that circle B has the same center as circle A and that the radius of circle B is two -5,5 times the radius of circle A. Therefore, the center of circle B is ^ h and the 2 5 10 - 10 radius of circle B is ^ h, or . Substituting 5 for t, 5 for u, and for r in the - 2+ - 2= 2 +5 2+ -5 2=102 equation ^x th ^y uh r yields ^x h ^y h , which is equivalent +5 2+ -5 2=100 to ^x h ^y h . It follows that the equation of circle B in the xy-plane is +5 2+ -5 2=100 ^x h ^y h . It’s also given that the equation defining circle B in the +5 2+ -5 2= xy-plane is ^x h ^y h k, where k is a constant. Therefore, the value of k 100 is . 39 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1
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