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
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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