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17 Sep 2018, 21:52
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
49% (02:16) correct
51%
(02:28)
wrong
based on 81
sessions
History
Date
Time
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Not Attempted Yet
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 2375 times ]
18 Sep 2018, 15:18
Kudos
Bookmarks
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.
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.
17 Feb 2020, 00:31
Kudos
Bookmarks
Bunuel
Solution:
- • Centre of the circle = \((1, 0)\)
• The radius of the circle = \(2\) Units
• \((x, y)\) lies on the circle.
• 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.
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.
