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In the xy-plane, a circle is centered at the point (-4,3) a

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In the xy-plane, a circle is centered at the point (-4,3) a [#permalink] New post 21 Dec 2017, 16:57
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In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π
B. 12π
C. 16π
D. 20π
E. 25π

kudo for the right solution and explanation
[Reveal] Spoiler: OA

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Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink] New post 22 Dec 2017, 02:41
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We can calculate the distrance from the point to the origin
Squroo (0 - (-4) + (0-3)
Squroot 4^2 + 3^2
Squroot 16 + 9
Squroot 25
Or 5 distance is 5
So the radius muss be 5 since it says that the origine lied on the circle.
Aera of circle is r^2*pi
So we have 25*pi so answer is E
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Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink] New post 22 Dec 2017, 06:39
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Popo wrote:
We can calculate the distrance from the point to the origin
Squroo (0 - (-4) + (0-3)
Squroot 4^2 + 3^2
Squroot 16 + 9
Squroot 25
Or 5 distance is 5
So the radius muss be 5 since it says that the origine lied on the circle.
Aera of circle is r^2*pi
So we have 25*pi so answer is E



Hi could you plz read before posting. Always check the spelling and mathematical expression-
https://greprepclub.com/forum/rules-for ... -1083.html
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Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink] New post 22 Dec 2017, 06:48
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Carcass wrote:
In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π
B. 12π
C. 16π
D. 20π
E. 25π

kudo for the right solution and explanation



Here,

Since the co-ordinates for the centre of the circle = (-4,3)

and it passes through the orgin i.e co ordinates are =(0,0)

NOw the distance from (-4,3) to point (0,0) will give the radius of the circle

Distance between two points (x1,y1) and (x2,y2) in the xy plane = \(\sqrt{{(x2 - x1)^2 + (y2 - y1)^2}}\)

Therefore the distance between (-4,3) and (0,0) = \(\sqrt{{(0 - (-4))^2 + (0 - 3)^2}}\)

=\(\sqrt{25}\) = 5

SInce Area of the circle = \(\pi * (radius)^2\)

= \(\pi * 5^2\)
=\(25\pi\) i. e option E
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Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink] New post 16 May 2018, 09:21
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Carcass wrote:
In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π
B. 12π
C. 16π
D. 20π
E. 25π


Since the circle is centered at the point (-4,3) and passes through the origin, we see that the radius is the hypotenuse of a triangle, with sides of 3 and 4, so we have a 3-4-5 right triangle with a hypotenuse of 5, which means the radius of the circle is also 5.

Thus, the area of the circle is π(5^2) = 25π,

Answer: E
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Re: In the xy-plane, a circle is centered at the point (-4,3) a   [#permalink] 16 May 2018, 09:21
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