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In the xy-plane , line l intersects a circle with center

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Intern
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In the xy-plane , line l intersects a circle with center [#permalink] New post 19 Aug 2013, 10:16
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  55% (medium)

Question Stats:

25% (02:29) correct 75% (01:11) wrong based on 36 sessions
In the xy-plane , line l intersects a circle with center at origin.Is the slope of line l equal to zero?

1) line l passes through second quadrant.

2) line l is perpendicular to the tangent of the circle.
[Reveal] Spoiler: OA
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GMAT 2: 670 Q50 V29
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Re: In the xy-plane , line l intersects a circle with center [#permalink] New post 19 Aug 2013, 11:04
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innocous wrote:
In the xy-plane , line l intersects a circle with center at origin.Is the slope of line l equal to zero?

1) line l passes through second quadrant.

2) line l is perpendicular to the tangent of the circle.


ALL LINES WHICH ARE PERPENDICULAR TO TANGENT WILL PASS THROUGH CENTRE.

IMO C.

SEE DIAG FOR EXPLANATION.
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Re: In the xy-plane , line l intersects a circle with center [#permalink] New post 22 Aug 2013, 03:47
In the xy-plane , line l intersects a circle with center at origin.Is the slope of line l equal to zero?

1) line l passes through second quadrant.
2) line l is perpendicular to the tangent of the circle.

FS1: Line l passing through second quadrant and intersecting the circle can be either parall to x-axis(in which case its slope is 0) or not parallel to x-axis(slope not eual to 0). Hence insufficient.
FS2: Line which is perpendicular to the tangent must pass thought centre (since angle betwwen radius and point of contact of tangent to a circle is 90 degrees). Hence, the line can have multiple possibilities for its slope (including 0 and infinity when the line is parallel to x or y axis respectively). Not sufficient.

Combining the above two, the only possibility is when the slope is negatice but not zero (x-axis is not in II quadrant). Hence slope iof line l is not zero for any case.
Sufficient. So answer should be C.
Re: In the xy-plane , line l intersects a circle with center   [#permalink] 22 Aug 2013, 03:47
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