Question the-eq
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?
The equation above defines a circle in the xy -plane. What are the coordinates of the
Hard-difficulty · SAT Math · Circles — Equation of a circle in coordinate plane. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice B is correct. The standard equation of a circle in the xy-plane is of the form 
, where 
are the coordinates of the center of the circle and r is the radius. The given equation can be rewritten in standard form by completing the squares. So the sum of the first two terms, 
, needs a 100 to complete the square, and the sum of the second two terms, 
, needs a 64 to complete the square. Adding 100 and 64 to both sides of the given equation yields 
, which is equivalent to 
. Therefore, the coordinates of the center of the circle are 
.
Choices A, C, and D are incorrect and may result from computational errors made when attempting to complete the squares or when identifying the coordinates of the center.
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