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SAT Math Practice Question #39035 - SATify | SATify

#39035

algebra

transformations

equations

circles

coordinate geometry

geometry

medium

75 sec

Calculator OK

A circle is defined by the equation $(x - a)^{2} + (y - b)^{2} = R^{2}$ , where $a$ , $b$ , and $R$ are positive constants. If this circle is translated in the xy-plane such that its new center is at the origin $(0, 0)$ , which of the following equations represents the translated circle?

A.

$(x + a)^{2} + (y + b)^{2} = R^{2}$

B.

$x^{2} + y^{2} = R^{2}$

C.

$(x - a)^{2} + (y - b)^{2} = 0$

D.

$(x - R)^{2} + (y - R)^{2} = 0$