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Is line tangent to circle ? 1. k + b = 1 2. k^2+b^2=1 (C)

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Is line tangent to circle ? 1. k + b = 1 2. k^2+b^2=1 (C) [#permalink]  29 Jun 2010, 04:36
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Quote:
Is line tangent to circle ?

1. k + b = 1
2. k^2+b^2=1
(C) 2008 GMAT Club - m17#12

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Statements (1) and (2) combined are insufficient. In equation , is the slope of the line while is the elevation (y-coordinate of the point where the line intersects with the vertical axis). Neither statement precludes the line from running through the origin . In this case, the line intersects circle at two points and thus is not tangent to it. However, if and , both statements are satisfied but the line only touches the circle at point . In this case, the line runs parallel to the x-axis.

I understand that S.1 is insufficient, as both k=1,b=0 and k=0,b=1 results in a line intersecting the circle
But how do I work out k^2+b^2=1 is insufficient?

Can someone direct me to a good learning page on circle properties?

Thanks,

HG
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Re: m17 Q 12 [#permalink]  29 Jun 2010, 06:12
Here's the link to the GMAT Club Math Book Circles Section:

math-circles-87957.html

Re: m17 Q 12   [#permalink] 29 Jun 2010, 06:12
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