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In the coordinate plane, a circle centered on point (-3, -4)

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by Gmat_mission » Sun Jun 30, 2019 9:15 am

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B

C

D

E

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Difficulty—

In the coordinate plane, a circle centered on point \((-3, -4)\) passes through the point \((1, 1).\) What is the area of the circle?

\(A.\ 9Ï€\)
\(B.\ 18Ï€\)
\(C.\ 25Ï€\)
\(D.\ 37Ï€\)
\(E.\ 41Ï€\)

[spoiler]OA=E[/spoiler]

Source: Veritas Prep
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by Scott@TargetTestPrep » Tue Jul 02, 2019 5:49 pm
Gmat_mission wrote:In the coordinate plane, a circle centered on point \((-3, -4)\) passes through the point \((1, 1).\) What is the area of the circle?

\(A.\ 9Ï€\)
\(B.\ 18Ï€\)
\(C.\ 25Ï€\)
\(D.\ 37Ï€\)
\(E.\ 41Ï€\)

[spoiler]OA=E[/spoiler]

Source: Veritas Prep
The distance between (-3, -4) and (1, 1) is the length of the radius. Therefore, let's determine the length of the radius using the distance formula:

r = √[(-3 - 1)^2 + (-4 - 1)^2] = √(16 + 25) = √41

Since the area of a circle is πr^2, the area of this circle is π(√41)^2 = 41π.

Answer: E

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