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In the xy-plane, circle C has center (1,0) and radius 2. If line k is

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In the xy-plane, circle C has center (1,0) and radius 2. If line k is  [#permalink]

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New post 02 Aug 2018, 22:38
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Question Stats:

68% (01:18) correct 32% (01:26) wrong based on 293 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).



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Re: In the xy-plane, circle C has center (1,0) and radius 2. If line k is  [#permalink]

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New post 03 Aug 2018, 01:12
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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
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Re: In the xy-plane, circle C has center (1,0) and radius 2. If line k is  [#permalink]

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New post 06 Sep 2018, 07:44
Don't mess with formulas in xy-plane questions: draw, draw, draw.

Answer D.
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Re: In the xy-plane, circle C has center (1,0) and radius 2. If line k is &nbs [#permalink] 06 Sep 2018, 07:44
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In the xy-plane, circle C has center (1,0) and radius 2. If line k is

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