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02 Aug 2018, 23:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:37) correct
25%
(01:47)
wrong
based on 2581
sessions
History
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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)
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) Line k passes through the point (−1,0).
(2) Line k passes through the point (−1,−1).
(DS01130)
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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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