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Math Expert V
Joined: 02 Sep 2009
Posts: 56370
In the xy-plane, circle C has center (1,0) and radius 2. If line k is  [#permalink]

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16 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:32) correct 33% (01:37) wrong based on 527 sessions

### HideShow timer Statistics 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).

NEW question from GMAT® Quantitative Review 2019

(DS01130)

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MBA Section Director V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2561
GPA: 4
WE: Engineering (Computer Software)
Re: In the xy-plane, circle C has center (1,0) and radius 2. If line k is  [#permalink]

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3
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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Senior Manager  G
Joined: 29 Dec 2017
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Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25
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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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1
Don't mess with formulas in xy-plane questions: draw, draw, draw.

Attachments 1.png [ 5.2 KiB | Viewed 3015 times ] Re: In the xy-plane, circle C has center (1,0) and radius 2. If line k is   [#permalink] 06 Sep 2018, 08:44
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# In the xy-plane, circle C has center (1,0) and radius 2. If line k is  