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Bunuel
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Where is the center of a circle on the xy plane? 31 Jan 2016, 08:26
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55% (hard)

Question Stats:

52% (01:21) correct 48% (01:32) wrong based on 221 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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E
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GMAT Focus 1: 735 Q90 V89 DI81
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Where is the center of a circle on the xy plane? 31 Jan 2016, 08:34
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Bunuel
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.
Show more

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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Where is the center of a circle on the xy plane? 06 Apr 2017, 19:11
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Bunuel
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.
Show more


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.
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Where is the center of a circle on the xy plane? 08 Nov 2018, 08:36
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Bunuel
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.
Show more

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.
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Where is the center of a circle on the xy plane? 08 Nov 2018, 08:37
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Argo
Bunuel
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.
Show more

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

Hence, E.
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Where is the center of a circle on the xy plane? 27 Nov 2019, 05:32
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