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In the xy-plane, find the area of a circle that has center (-4, 1), an

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In the xy-plane, find the area of a circle that has center (-4, 1), an  [#permalink]

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New post 28 Mar 2018, 03:00
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Question Stats:

91% (01:26) correct 9% (00:46) wrong based on 53 sessions

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In the xy-plane, find the area of a circle that has center (-4, 1), an  [#permalink]

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New post 28 Mar 2018, 04:26
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Bunuel wrote:
In the xy-plane, find the area of a circle that has center (-4, 1), and passes through the point (2, -5)?

(A) \(12\pi\)
(B) \(20\pi\)
(C) \(40\pi\)
(D) \(52\pi\)
(E) \(72\pi\)



r of the circle = distance b/w points

dist = rt [(2+4) + (-5-1)} = 6rt2

e imo
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In the xy-plane, find the area of a circle that has center (-4, 1), an  [#permalink]

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New post 28 Mar 2018, 09:22
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Bunuel wrote:
In the xy-plane, find the area of a circle that has center (-4, 1), and passes through the point (2, -5)?

(A) \(12\pi\)
(B) \(20\pi\)
(C) \(40\pi\)
(D) \(52\pi\)
(E) \(72\pi\)

Standard equation of a circle, where (h,k), are center coordinates:

\((x - h)^2 + (y - k)^2 = r^2\)
\((h,k) = (-4,1)\)
\((x + 4)^2 + (y - 1)^2 = r^2\)


Insert (2,-5) into the equation to find \(r^2\).
\((2 + 4)^2 + (-5-1)^2 = r^2\)
\(6^2 + 6^2 = r^2\)
\(r^2 = 72\)

Leave \(r^2\)

Area = \(\pi r^2 =72\pi\)

Answer E
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Re: In the xy-plane, find the area of a circle that has center (-4, 1), an  [#permalink]

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New post 28 Mar 2018, 10:23
Bunuel wrote:
In the xy-plane, find the area of a circle that has center (-4, 1), and passes through the point (2, -5)?

(A) \(12\pi\)
(B) \(20\pi\)
(C) \(40\pi\)
(D) \(52\pi\)
(E) \(72\pi\)


Formula of square of a circle = \(pi*r^2\)
here radius. r = the distance between centre and the given point(2, -5)

We know, the distance between two points = \(\sqrt{(X1 - X2)^2 + (Y1-Y2)^2}\)

so r = \(\sqrt{(-4-2)^2 + (1- (-5))^2}\)
So, the area = \(pi*r^2\) = \(72pi\)
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Re: In the xy-plane, find the area of a circle that has center (-4, 1), an   [#permalink] 28 Mar 2018, 10:23
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