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In the coordinate plane, a circle has center (2, -3)

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In the coordinate plane, a circle has center (2, -3)

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In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π
OA is E
Experts, Can you give me some help here? Please.

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Since the area of a circle is $$\pi\cdot r^2$$ we have to find r.

Using the formula of distance between two points in the plane, we have that $$r=d\left(\left(2,-3\right);\left(5,0\right)\right)=\sqrt{\left(5-2\right)^2+\left(0-\left(-3\right)\right)^2}=\sqrt{3^2+3^2}$$ $$\Rightarrow\ r=\sqrt{9\cdot2}=3\sqrt{2}$$ and therefore the area is $$A=\ \pi\cdot\left(3\sqrt{2}\right)^2=18\pi$$ Hence, the answer is E.

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