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Bunuel
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A circle with center (1, 0) lies in the coordinate plane shown above. 18 Jun 2022, 19:30
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C
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Difficulty:

75% (hard)

Question Stats:

44% (02:55) correct 56% (02:24) wrong based on 34 sessions

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A circle with center (1, 0) lies in the coordinate plane shown above. If points (x, y) and (3, 0) lie on the circle is (x, y) in quadrant 1?

(1) –1 < y < 1
(2) –1 < x < 1


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C
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SaquibHGMATWhiz
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A circle with center (1, 0) lies in the coordinate plane shown above. 21 Jun 2022, 06:48
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The picturization is key in this question to make it easy.




    As per the question stem, we know -
      (1,0) and (3,0) are centers and a point on the circle.
      Thus we can say that the radius is 2. (Since the y coordinates are 0 for both the cases, the difference between the y coordinates will be the radius so no need to use a formula)

    So, we can say that the top most point of the circle would be (1,2)

Statement 1:

–1 < y < 1

    Any point with the y coordinate between -1 and 1 can still be on the circumference.
      So the part denoted by red are the points within the range having y coordinate between -1 to 1 and out of which the part denoted in black in the first quadrant.
      However, any other point will not be in the first quadrant.

So we can get (x,y) on the first quadrant in some scenarios, and in others, we won't.

We eliminate options A and D.

Statement 2:

–1 < x < 1

    Any point with the x coordinate between -1 and 1 can still be on the circumference.
      Very similar to the previous one, the part denoted in green is within the given range. However, only the black part is in the first quadrant.

So we can get (x,y) on the first quadrant in some scenarios, and in others, we won't.

We eliminate option B.

When we combine we do not get any common area (the black from the first and black from the second scenario do not have anything common) and hence we can say the answer as 'NO', (x, y) do not line on the circumference.

The answer is C.


Please excuse the image part.
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Bunuel
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