SAT Math Multiple Choice Question 71: Answer and Explanation

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Question: 71

11. Which of the following is a possible equation for a circle that is tangent to both the x-axis and the line x = 4 ?

  • A. (x + 2)2 + (y + 2)2 = 4
  • B. (x + 2)2 + (y - 2)2 = 4
  • C. (x - 2)2 + (y + 4)2 = 4
  • D. (x - 6)2 + (y - 2)2 = 4

Correct Answer: D

Explanation:

D All the answer choices are equal to 4 (which is r2, making r = 2), so you need to focus on where the center of the circle lies. If the circle is tangent to both the x axis (which is equivalent to the line y = 0) and the line x = 4, then the center must be 2 units from y = 0 and 2 units from x = 4. Choices (A) and (B) both have centers with an x value of -2 (remember the standard form of the circle equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius), which is 6 units from x = 4. Eliminate (A) and (B). Choice (C) has a center at (2, -4). The x value is 2 units from x = 4; however, the y value is 4 units from y = 0. Eliminate (C) and choose (D).

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