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

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Joined: 02 Sep 2009
Posts: 44599
In the xy-plane, find the area of a circle that has center (-4, 1), an [#permalink]

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28 Mar 2018, 03:00
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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) $$72\pi$$
[Reveal] Spoiler: OA

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Location: India
GMAT 1: 710 Q49 V36
In the xy-plane, find the area of a circle that has center (-4, 1), an [#permalink]

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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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Joined: 22 May 2016
Posts: 1546
In the xy-plane, find the area of a circle that has center (-4, 1), an [#permalink]

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28 Mar 2018, 09:22
1
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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 = $$\pi r^2 =72\pi$$

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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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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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