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M17 Q12

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Manager
Manager
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Joined: 16 Jul 2009
Posts: 248

Kudos [?]: 440 [0], given: 3

M17 Q12 [#permalink]

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New post 02 Jun 2010, 01:46
Is line y=kx+b tangent to circle \(x^2 + y^2\) = 1?

1. k+b = 1
2. \(k^2+b^2\) = 1

Statements (1) and (2) combined are insufficient. In equation y=kx+b, 'k' is the slope of the line while 'b' 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 (b=0,k=1). In this case, the line intersects circle \(x^2+y^2 = 1\) at two points and thus is not tangent to it. However, if k=0 and b=1, both statements are satisfied but the line only touches the circle at point (0,1). In this case, the line runs parallel to the x-axis.

If line (b=0,k=1) intersects the circle at two points, then how does line (k=0,b=1) intersects only at (0,1). Moreover, if we know that the both options created by st2 are not tangent to the circle but intersect the circle then the OA might as well be 'B'. Am I missing something here?

Please explain.

Kudos [?]: 440 [0], given: 3

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Joined: 08 Apr 2009
Posts: 1199

Kudos [?]: 476 [0], given: 19

Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
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Re: M17 Q12 [#permalink]

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New post 09 Jun 2010, 02:01
k=0,b=1 is tangent to the circle.
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Kudos [?]: 476 [0], given: 19

Re: M17 Q12   [#permalink] 09 Jun 2010, 02:01
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M17 Q12

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