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In the coordinate plane, a circle has center (2, -3) and

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In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 16 Dec 2009, 03:20
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In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Apr 2012, 00:35, edited 1 time in total.
Edited the question and added the OA
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Re: Coordinate Geometry from Paper test [#permalink] New post 16 Dec 2009, 03:24
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IMO E ---> 18 pi

r=sqrt[{5-2}^2+{0+3}^2]=3 sqrt2.......(dist formula)
area=pi r^2
=pi* (3 sqrt2)^2=18 pi

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Re: Coordinate Geometry from Paper test [#permalink] New post 16 Dec 2009, 08:51
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E - 18pi

r^2 = [(5-2)^2 + (-3-0)^2] = 18. So Area = pi * r^2 = 18pi
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Re: Coordinate Geometry from Paper test [#permalink] New post 17 Dec 2009, 03:30
xcusemeplz2009 wrote:
IMO E ---> 18 pi

r=sqrt[{5-2}^2+{0+3}^2]=3 sqrt2.......(dist formula)
area=pi r^2
=pi* (3 sqrt2)^2=18 pi


hi can u elaborate what u mean by dis formula

thanks
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Re: Coordinate Geometry from Paper test [#permalink] New post 17 Dec 2009, 03:55
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OA is E

The distance formula in coordinate geometry is used to calculate the distance between 2 points whose coordinates are given

Lets say we have to calculate the distance between 2 points (x1, y1) and (x2, y2)

It is given by -

sqrt [ (x2-x1)^2 + (y2-y1)^2]

In this case since we are given the coordinates of the center and the fact that the circle passes thru (5,0), we can calculate the radius (needed for finding the area of the circle), by calculating the distance from the center to point (5,0)

Hope this helps

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Re: Coordinate Geometry from Paper test [#permalink] New post 09 Jan 2010, 22:52
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Got E. Used distance formula. Didn't solve for hypotenuse since it was an isoceles right triangle. Plugged in 3 sqrt 2 for radius in area formula. Thanks for the post. Got the answer pretty quickly. What level would you say this is?

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Re: Coordinate Geometry from Paper test [#permalink] New post 09 Jan 2010, 23:00
gottabwise wrote:
Got E. Used distance formula. Didn't solve for hypotenuse since it was an isoceles right triangle. Plugged in 3 sqrt 2 for radius in area formula. Thanks for the post. Got the answer pretty quickly. What level would you say this is?


Just copied problem into notes and recognized how I did extra work...should've just did distance formula b/w (5,0) and (2,-3)...r^2=(5-2)^3+(0--3)^2=sqrt18=3sqrt2. I guess that's why I'm reviewing right now. :| Noticing that r^2 doesn't need to be solved for either.

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Re: Coordinate Geometry from Paper test [#permalink] New post 02 Apr 2012, 00:01
zaarathelab wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π


Can any body draw the picture for this

i thought y coordinate between (5,0) & (2,-3) will be radius i.e 3
and area will be 3*3pie

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Re: Coordinate Geometry from Paper test [#permalink] New post 02 Apr 2012, 00:34
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GMATD11 wrote:
zaarathelab wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π


Can any body draw the picture for this

i thought y coordinate between (5,0) & (2,-3) will be radius i.e 3
and area will be 3*3pie


The point is that the radius does not equal to 3, it equals to 3\sqrt{2}. You can find the length of the radius either with the distance formula (the formula to calculate the distance between two points (x_1,y_1) and (x_2,y_2) is d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}) or with Pythagoras theorem. Look at the diagram below:
Attachment:
graph.png
graph.png [ 10.12 KiB | Viewed 6823 times ]
The radius of the circle is the hypotenuse of a right isosceles triangle with the legs equal to 3: r^2=3^2+3^2=18 --> area=\pi{r^2}=18\pi.

Answer: E.

Hope it helps.

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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 04 Apr 2012, 04:26
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E

we get height as "3" using points (2,0) & (2,-3)

we get base as "3" using points (2,0) & (5,0)

therefore (radius)^2 = (3)^2 + (3)^2
radius = 3sqrt2

area = pi * r*r
=18pi
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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 12 Aug 2013, 03:03
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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 12 Aug 2013, 04:58
zaarathelab wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π

.
fastest way is to use the distance law between two coordinators.

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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 10 Nov 2013, 17:04
The equation of a circle is given by the formula (x-a)^2+(y-b)^2=r^2 where a and b represent the coordinates of the centre and r the radius. Substituting we get (x-2)^2+(y+3)^2=r^2. Now, given that the circle passes through the points (5,0). Hence, the when we substitute x=5 and y=0 in the equation above it should be satisfied. Substituting we get (5-2)^2+(0+3)^2=r^2. Therefore r^2=18. Area=pi*r^2=18pi.
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Re: Coordinate Geometry from Paper test [#permalink] New post 19 Dec 2013, 00:13
Bunuel wrote:
GMATD11 wrote:
zaarathelab wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π


Can any body draw the picture for this

i thought y coordinate between (5,0) & (2,-3) will be radius i.e 3
and area will be 3*3pie


The point is that the radius does not equal to 3, it equals to 3\sqrt{2}. You can find the length of the radius either with the distance formula (the formula to calculate the distance between two points (x_1,y_1) and (x_2,y_2) is d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}) or with Pythagoras theorem. Look at the diagram below:
Attachment:
graph.png
The radius of the circle is the hypotenuse of a right isosceles triangle with the legs equal to 3: r^2=3^2+3^2=18 --> area=\pi{r^2}=18\pi.

Answer: E.

Hope it helps.


But if the radius = hypothenuse, and if hypothenuse = 18, then the area is 18*18*pi, not 18*pi.. Right? Or am I missing something?
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Re: Coordinate Geometry from Paper test [#permalink] New post 19 Dec 2013, 00:17
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aeglorre wrote:
Bunuel wrote:
GMATD11 wrote:

Can any body draw the picture for this

i thought y coordinate between (5,0) & (2,-3) will be radius i.e 3
and area will be 3*3pie


The point is that the radius does not equal to 3, it equals to 3\sqrt{2}. You can find the length of the radius either with the distance formula (the formula to calculate the distance between two points (x_1,y_1) and (x_2,y_2) is d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}) or with Pythagoras theorem. Look at the diagram below:
Attachment:
graph.png
The radius of the circle is the hypotenuse of a right isosceles triangle with the legs equal to 3: r^2=3^2+3^2=18 --> area=\pi{r^2}=18\pi.

Answer: E.

Hope it helps.


But if the radius = hypothenuse, and if hypothenuse = 18, then the area is 18*18*pi, not 18*pi.. Right? Or am I missing something?


No. Notice that we get that r^2=18, not r. Thus area=\pi{r^2}=18\pi.

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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 25 Jun 2014, 21:30
I used Ballpark method :
(x,y) = center (2,-3) to circumference of circle (5,0) that means radius should be more than 3. let's say 3+
area = π*r^2, should be more than π*3^2 ;
answer > 9π only 18π is eligible.
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In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 19 Jul 2014, 21:59
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In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π

The Question is locked

Question Discussed here : in-the-coordinate-plane-a-circle-has-center-2-3-and-88057.html

Last edited by WoundedTiger on 20 Jul 2014, 03:29, edited 1 time in total.
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Re: In the coordinate plane, a circle has center (2, -3) and [#permalink] New post 20 Jul 2014, 05:10
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iyersu wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π

The Question is locked

Question Discussed here : in-the-coordinate-plane-a-circle-has-center-2-3-and-88057.html


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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the coordinate plane, a circle has center (2, -3) and   [#permalink] 20 Jul 2014, 05:10
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