SAT Mathematics Practice Test 5

The standard equation of a circle in the xy−plane is of the form (x−h)2+(y−k)2=r2, where(h,k) are the coordinates of the center of the circle and r is the radius. To convert the given equation to the standard form, complete the squares. The first two terms need a 100 to complete the square, and the second two terms need a 64. Adding 100 and 64 to both sides of the given equation yields ,which is equivalent to (x+10)2(y+8)2=144.Therefore, the coordinates of the center of the circle are (−10,−8).Choice A is incorrect and is likely the result of not properly dividing when attempting to complete the square. Choice C is incorrect and is likely the result of making a sign error when evaluating the coordinates of the center. Choice D is incorrect and is likely the result of not properly dividing when attempting to complete the square and making a sign error when evaluating the coordinates of the center.