sat-dog

Choice D is correct. The graph in the xy-plane of an equation of the form ( - )2+( - )2= 2 ( ) x h y k r is a circle with center h, k and a radius of length r. It’s 2+( - )2= given that circle A is represented by x y 1 49, which can be rewritten as 2+( - )2= 2 ( ) x y 1 7 . Therefore, circle A has center 0, 1 and a radius of length 7. Shifting circle A down two units is a rigid vertical translation of circle A that does not change its size or shape. Since circle B is obtained by shifting circle A down two units, it follows that circle B has the same radius as circle A, and for each point ( ) ( - ) ( ) x, y on circle A, the point x, y 2 lies on circle B. Moreover, if h, k is the ( - ) center of circle A, then h, k 2 is the center of circle B. Therefore, circle B has a ( - ) ( - ) radius of 7 and the center of circle B is 0, 1 2 , or 0, 1. Thus, circle B can be 2+( + )2= 2 2+( + )2= represented by the equation x y 1 7 , or x y 1 49. Choice A is incorrect. This is the equation of a circle obtained by shifting circle A right 2 units. Choice B is incorrect. This is the equation of a circle obtained by shifting circle A up 2 units. Choice C is incorrect. This is the equation of a circle obtained by shifting circle A left 2 units.