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#20411

transformations

circles

hard

240 sec

Circle A, a circle with its center at $(0, 5)$ and a radius of $2$ , is defined by the equation $x^{2} + (y - 5)^{2} = 4$ . Circle B (not shown) is the result of shifting circle A left $4$ units and down $7$ units, and increasing the radius so that the radius of circle B is $3$ times the radius of circle A. Which equation defines circle B ?

A.

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

B.

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

C.

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

D.

$(x + 4)^{2} + (y + 2)^{2} = (3) (2)$