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02 Aug 2018, 23:38
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D
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Difficulty:
25%
(medium)
Question Stats:
75% (01:37) correct
25%
(01:47)
wrong
based on 2537
sessions
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In the xy-plane, circle C has center (1,0) and radius 2. If line k is parallel to the y-axis, is line k tangent to circle C ?
(1) Line k passes through the point (−1,0).
(2) Line k passes through the point (−1,−1).
(DS01130)
(1) Line k passes through the point (−1,0).
(2) Line k passes through the point (−1,−1).
(DS01130)
03 Aug 2018, 02:12
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To find if line K is tangent to the circle C
line k is parallel to the y-axis
Statement 1
Line k passes through the point (−1,0).
Since the line passes though (-1,0) and the line is parallel to y axis, the equation of the line is x = -1
Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1
Hence the line is tangent to the circle
Statement 1 is sufficient
Statement 2
Line k passes through the point (−1,−1).
Since the line passes though (-1,-1) and the line is parallel to y axis, the equation of the line is x = -1 => the line also passes through (-1,0-)
Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1
Hence the line is tangent to the circle
Statement 2 is sufficient
Hence option D
line k is parallel to the y-axis
Statement 1
Line k passes through the point (−1,0).
Since the line passes though (-1,0) and the line is parallel to y axis, the equation of the line is x = -1
Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1
Hence the line is tangent to the circle
Statement 1 is sufficient
Statement 2
Line k passes through the point (−1,−1).
Since the line passes though (-1,-1) and the line is parallel to y axis, the equation of the line is x = -1 => the line also passes through (-1,0-)
Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1
Hence the line is tangent to the circle
Statement 2 is sufficient
Hence option D
06 Sep 2018, 08:44
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Don't mess with formulas in xy-plane questions: draw, draw, draw.
Answer D.
Answer D.
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