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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Where is the center of a circle on the xy plane?  [#permalink]

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10 00:00

Difficulty:   65% (hard)

Question Stats: 51% (01:23) correct 49% (01:35) wrong based on 187 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 V
Joined: 02 Aug 2009
Posts: 8288
Re: Where is the center of a circle on the xy plane?  [#permalink]

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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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Manager  B
Joined: 03 Jul 2016
Posts: 65
Re: Where is the center of a circle on the xy plane?  [#permalink]

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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  P
Joined: 31 Jul 2017
Posts: 508
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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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  P
Joined: 31 Jul 2017
Posts: 508
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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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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Posts: 13724
Re: Where is the center of a circle on the xy plane?  [#permalink]

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_________________ Re: Where is the center of a circle on the xy plane?   [#permalink] 27 Nov 2019, 05:32
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