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#20410

transformations

circles

hard

240 sec

Circle A, a circle with its center at $(3, - 1)$ and a radius of $4$ , is defined by the equation $(x - 3)^{2} + (y + 1)^{2} = 16$ . Circle B (not shown) is the result of shifting circle A right $5$ units and up $3$ units, and increasing the radius so that the radius of circle B is $1.5$ times the radius of circle A. Which equation defines circle B ?

A.

$(x - 8)^{2} + (y - 2)^{2} = (9/4) (16)$

B.

$(x + 8)^{2} + (y + 2)^{2} = (9/4) (16)$

C.

$(x - 8)^{2} + (y + 2)^{2} = (9/4) (16)$

D.

$(x - 8)^{2} + (y - 2)^{2} = (1.5) (4)$