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Manager  Joined: 22 Sep 2010
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What is the equation of a circle of radius 6 units centered  [#permalink]

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Question Stats: 63% (01:22) correct 37% (01:40) wrong based on 336 sessions

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What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x^2 + y^2 + 6x – 4y = 23
B. x^2 + y^2 - 6x + 4y = 23
C. x^2 + y^2 + 6x + 4y = 23
D. x^2 + y^2 - 6x – 4y = - 23
E. x^2 + y^2 - 6x – 4y = 23

Originally posted by pzazz12 on 01 Oct 2010, 04:38.
Last edited by Bunuel on 29 Dec 2013, 16:09, edited 1 time in total.
Renamed the topic and edited the question.
Manager  Joined: 30 Aug 2010
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Re: equation of a circle...  [#permalink]

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the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2

=> answer = (X-3)^2+(Y-2)^2=6^2

solving,,we get the equation in answer choice "E".
Retired Moderator Joined: 02 Sep 2010
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Re: equation of a circle...  [#permalink]

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you might find this post about equations of various geometries a useful refresher
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Manager  Joined: 22 Sep 2010
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Equation of a circle.......  [#permalink]

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What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x – 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x – 4y = - 23
E. x2 + y2 - 6x – 4y = 23
Retired Moderator Joined: 02 Sep 2010
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Location: London
Re: Equation of a circle.......  [#permalink]

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The equation will be :
$$(x-3)^2+(y-2)^2=6^2$$
If you simplify this, you'll get (e) Posted from GMAT ToolKit
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Director  G
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Re: What is the equation of a circle of radius 6 units centered  [#permalink]

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pzazz12 wrote:
What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x^2 + y^2 + 6x – 4y = 23
B. x^2 + y^2 - 6x + 4y = 23
C. x^2 + y^2 + 6x + 4y = 23
D. x^2 + y^2 - 6x – 4y = - 23
E. x^2 + y^2 - 6x – 4y = 23

Just did backsolving by picking one point in circle such as (9, 2)

Option C where all summed is not true, so it must be options with subtracting.

Chose E and it is correct

E
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Re: What is the equation of a circle of radius 6 units centered  [#permalink]

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Answer E by simplifying circle equation: (x−3)^2+(y−2)^2=6^2
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Re: What is the equation of a circle of radius 6 units centered  [#permalink]

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Hi,

Is this type of question is part of GMAT as have never seen such question in official book or in the books of Manhattan.
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: What is the equation of a circle of radius 6 units centered  [#permalink]

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Coordinate geometry is a part of GMAT as per the conventional wisdom, but I guess it would be unlikely to see such a direct formula based question on the real exam. But you never know But having said all that, it is still not too different from questions which do show up on the real exam - viz. coordinate geometry with lines. So it would do no harm to try and understand how the problem can be tackled. You can find all you need about this problem here.

If you know that the equation of a circle centered at (a,b) with a radius of r is -
$$(x-a)^2 + (y-b)^2 = r^2$$

This question then becomes a piece of cake.

we surely are expecting middle terms in the binary squares to have negative coefficients - and hence all except D & E are eliminated at first sight. Now, the constant terms of the two binomial expansions will add up to 13 (3^2 + 2^2) and hence the RHS will be 36 - 13 or 23. Hence Option (E) is correct.

Gmatprep550 wrote:
Hi,

Is this type of question is part of GMAT as have never seen such question in official book or in the books of Manhattan.

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Re: What is the equation of a circle of radius 6 units centered  [#permalink]

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Thanks a ton Gladiator59

Coordinate geometry is a part of GMAT as per the conventional wisdom, but I guess it would be unlikely to see such a direct formula based question on the real exam. But you never know But having said all that, it is still not too different from questions which do show up on the real exam - viz. coordinate geometry with lines. So it would do no harm to try and understand how the problem can be tackled. You can find all you need about this problem here.

If you know that the equation of a circle centered at (a,b) with a radius of r is -
$$(x-a)^2 + (y-b)^2 = r^2$$

This question then becomes a piece of cake.

we surely are expecting middle terms in the binary squares to have negative coefficients - and hence all except D & E are eliminated at first sight. Now, the constant terms of the two binomial expansions will add up to 13 (3^2 + 2^2) and hence the RHS will be 36 - 13 or 23. Hence Option (E) is correct.

Gmatprep550 wrote:
Hi,

Is this type of question is part of GMAT as have never seen such question in official book or in the books of Manhattan.

_________________
______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere and help me to learn  Re: What is the equation of a circle of radius 6 units centered   [#permalink] 20 Jan 2019, 04:47
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