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# Where is the center of a circle on the xy plane?

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Math Expert
Joined: 02 Sep 2009
Posts: 61282
Where is the center of a circle on the xy plane?  [#permalink]

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31 Jan 2016, 07:26
1
10
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:22) correct 49% (01:34) wrong based on 193 sessions

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Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

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Math Expert
Joined: 02 Aug 2009
Posts: 8261
Re: Where is the center of a circle on the xy plane?  [#permalink]

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31 Jan 2016, 07:34
3
1
Bunuel wrote:
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

Hi,
Easy to make mistake, if done in a hurry, in these Q

Since no info in the Q stem, lets see the choices..
(1) The circle passes through both the origin and (0,7).
we may take this to be a diameter and thik it to be sufficient..
But it can be a chord or a diameter, so INSUFF

(2) The diameter equals 10.
clearly insuff

Combined..
we may take it to be sufficient as we know legth of a chord along with the coordinates and the dia too..
But we are not aware if the chord is below the dia or above the dia..
Accordingly the origin will change

E
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Posts: 65
Re: Where is the center of a circle on the xy plane?  [#permalink]

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06 Apr 2017, 18:11
Bunuel wrote:
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

Suppose (x,y) is the centre of the circle. So the radius r can be defined as distance between the centre and any point on the circle.

So, x^2 +y^2 = x^2 + (y-7)^2 --> equation 1 from the statement 1. From this, we get the value of y.

From statement 2, diameter = 2r and since r^2 = x^2 +y^2 from statement 1 and we know the value of y, we can find x.

So, isn't C the answer? Correct me if I am wrong.
Director
Joined: 31 Jul 2017
Posts: 502
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Where is the center of a circle on the xy plane?  [#permalink]

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08 Nov 2018, 07:36
Bunuel wrote:
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

The equation of Circle is -

$$(x-h)^2 + (y-k)^2 = r^2$$, where h & k are center of Circle.

Statement I:

The Circle passes through (0,0) & (0,7), We have -

$$r^2 = h^2 + k^2$$ and $$r^2 = h^2 + (7-k)^2$$. From these two equation, we have -

$$h^2 + k^2 = h^2 + (7-k)^2$$

$$k = 3.5$$, But we can't find h. Hence, Insufficient.

Statement II:

Only radius is given So, Insufficient.

Combining the two we have -

$$k = 3.5, r = 5.$$

As the circle passes through (0,0)..

$$r^2 = h^2 + k^2$$

Here, h can be both positive and negative for given value of k & r.

Hence, Insufficient.

E.
Director
Joined: 31 Jul 2017
Posts: 502
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Where is the center of a circle on the xy plane?  [#permalink]

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08 Nov 2018, 07:37
Argo wrote:
Bunuel wrote:
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

Suppose (x,y) is the centre of the circle. So the radius r can be defined as distance between the centre and any point on the circle.

So, x^2 +y^2 = x^2 + (y-7)^2 --> equation 1 from the statement 1. From this, we get the value of y.

From statement 2, diameter = 2r and since r^2 = x^2 +y^2 from statement 1 and we know the value of y, we can find x.

So, isn't C the answer? Correct me if I am wrong.

You can find X. But it can be both positive & negative.

Hence, E.
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Re: Where is the center of a circle on the xy plane?  [#permalink]

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27 Nov 2019, 04:32
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Re: Where is the center of a circle on the xy plane?   [#permalink] 27 Nov 2019, 04:32
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