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A circle in the $x y$-plane has center $(5,7)$ and radius 2. Which of the following is an equation of the circle?

SAT · Math · previous-year question

  1. A.$(x-5)^{2}+(y-7)^{2}=4$correct
  2. B.$(x+5)^{2}+(y+7)^{2}=4$
  3. C.$(x-5)^{2}+(y-7)^{2}=2$
  4. D.$(x+5)^{2}+(y+7)^{2}=2$

Answer

A. $(x-5)^{2}+(y-7)^{2}=4$

Explanation

Choice A is correct. A circle in the $x y$-plane with center $(h, k)$ and radius $r$ is defined by the equation $(x-h)^{2}+(y-k)^{2}=r^{2}$. Therefore, an equation of a circle with center $(5,7)$ and radius 2 is $(x-5)^{2}+(y-7)^{2}=2^{2}$, or $(x-5)^{2}+(y-7)^{2}=4$.Choice B is incorrect. This equation defines a circle with center $(-5,-7)$ and radius 2 . Choice $\mathrm{C}$ is incorrect. This equation defines a circle with center $(5,7)$ and radius $\sqrt{2}$. Choice $D$ is incorrect. This equation defines a circle with center $(-5,-7)$ and radius $\sqrt{2}$.

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