PSAT Math Multiple-Choice Question 159: Answer and Explanation

Question: 159

A circle is graphed in the xy-plane. If a circle has center (-3, 5) and a radius of 4, which of the following could be an equation of the circle?

• A. (x - 3)² - (y - 5)² = 4
• B. (x - 3)² + (y - 5)² = 4
• C. (x + 3)² - (y - 5)² = 16
• D. (x + 3)² + (y - 5)² = 16

Correct Answer: D

Explanation:

D

The question asks for the equation of a circle. The equation of a circle can be written in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius of the circle. Eliminate (A) and (C), which have subtraction between the binomials instead of addition. Look at the two remaining choices. The choices differ both in the center and in the radius, so eliminate one choice using any of this information. Since the center is (-3, 5), h = -3 and (x - h) = (x + 3). Also, since the radius is 4, r² = 16. Using either of those pieces, eliminate (B). The correct answer is (D).