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# A circle with center (1, 0) and radius 2 lies in the coordinate plane

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Math Expert
Joined: 02 Sep 2009
Posts: 62285
A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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17 Sep 2018, 20:52
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Difficulty:

85% (hard)

Question Stats:

49% (02:25) correct 51% (02:28) wrong based on 57 sessions

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A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle is (x, y) in quadrant 2?

(1) |y| > 1
(2) |x| > 1

Attachment:

image017.jpg [ 1.42 KiB | Viewed 850 times ]

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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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18 Sep 2018, 14:18
3
1
i recommend sketching the circle with radius 2 and center (1,0)

1: either
y >1 --> it could be in quadrant 1 or 2 already NS, no need to look further
but lets do it anyway
or
y < -1 -> it could be in quadrant 3 or 4 (still see y>1, so NS)

2)
x is > 1 --> it could be in quadrant 1 or 4 --> sufficient so far
x is < -1 --> point has to be on the circle, since the circle has radius 2 and center 1,0
point -1,0 is the lefternmost point on the circle however this lies on the X axis, and does not belong to a quadrant, so it does not lie in Q2

Sufficient

B

kudos if this helped.
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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16 Feb 2020, 23:31
Bunuel wrote:

A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle is (x, y) in quadrant 2?

(1) |y| > 1
(2) |x| > 1

Attachment:
image017.jpg

Solution:

• Centre of the circle = $$(1, 0)$$
• The radius of the circle = $$2$$ Units

• $$(x, y)$$ lies on the circle.
We need to find the whether $$(x, y)$$ is in second quadrant or not.
• Whether x < 0 and y > 0 or not
Statement 1: $$|y| > 1$$
• $$y < -1$$ or $$y > 1$$
• If $$y < -1$$, then $$(x, y)$$ lies in either in $$III$$ or $$IV$$ quadrant.
• If $$y > 1$$, then $$(x, y)$$ lies in either $$I$$ or $$II$$ quadrant.
Hence, statement 1 is not sufficient, we can eliminate the answer option A and D.
Statement 2: $$|x| > 1$$
• $$x < -1$$ or $$x > 1$$
• If $$x > 1$$, then $$(x, y)$$ lies in either $$I$$ or $$IV$$ quadrant.
• If $$x < -1$$, then $$(x, y)$$ does not lies on the circle. it means $$x$$ cannot be less than $$-1$$, we can discard this case.
o We can surely say that $$(x, y)$$ does not lies in $$II$$ or $$III$$ quadrant.
Hence, the correct answer is Option B.
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane   [#permalink] 16 Feb 2020, 23:31
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