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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]  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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Manager
Joined: 25 Nov 2017
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Kudos [?]: 40 [1] , given: 5

Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink]  22 Dec 2017, 02:41
1
KUDOS
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
Director
Joined: 20 Apr 2016
Posts: 727
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Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink]  22 Dec 2017, 06:39
1
KUDOS
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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Director
Joined: 20 Apr 2016
Posts: 727
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Kudos [?]: 475 [1] , given: 82

Re: In the xy-plane, a circle is centered at the point (-4,3) a [#permalink]  22 Dec 2017, 06:48
1
KUDOS
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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Target Test Prep Representative
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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
1
KUDOS
Expert's post
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,

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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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