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#40078

transformations

circles

hard

240 sec

Circle A (shown), a circle with its center at $(- 2, 0)$ and a radius of $3$ , is defined by the equation $(x + 2)^{2} + y^{2} = 9$ . Circle B (not shown) is the result of shifting circle A right $3$ 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.

$(x - 1)^{2} + y^{2} = 20.25$

B.

$(x + 1)^{2} + y^{2} = 20.25$

C.

$(x - 1)^{2} + y^{2} = 13.5$

D.

$(x + 2)^{2} + (y - 3)^{2} = 20.25$