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Is line y = kx + b tangent to circle x^2 + y^2 = 1 ? 1. k +

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Is line y = kx + b tangent to circle x^2 + y^2 = 1 ? 1. k + [#permalink] New post 30 Aug 2008, 03:34
Is line y = kx + b tangent to circle x^2 + y^2 = 1 ?

1. k + b = 1
2. k^2 + b^2 = 1
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Re: coordinate geometry [#permalink] New post 30 Aug 2008, 03:47
E

Consider two simple examples that satisfy both conditions:

a) k=1, b=0: y=x - goes thorough (0,0) point and intersect the circle at two points. false.
b) k=0, b=1: y=1 - is a tangent of the circle. true.
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Re: coordinate geometry [#permalink] New post 30 Aug 2008, 04:45
:wink: .. whenever i see ur bike...
i dont know which is faster...
ur mind or the bike....

take a bow serg!!! :beer
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Re: coordinate geometry [#permalink] New post 30 Aug 2008, 04:54
I've just finished my draft of one of HBS essays and decided to relax a bit at math forum :)
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Re: coordinate geometry [#permalink] New post 30 Aug 2008, 05:23
walker wrote:
I've just finished my draft of one of HBS essays and decided to relax a bit at math forum :)
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Walker = Ultimate Math Machine
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Re: coordinate geometry [#permalink] New post 03 Sep 2008, 08:27
If you consider both statements together:
k+b = 1; b=1-k; b^2 = (1-k)^2 = 1+k^2-2k
k^2+b^2 = 1; b^2= 1-k^2
Therefore, 1+k^2-2k = 1-k^2
On solving we get,
k=1
If k=1, b=0
Substituting these values in the equation y= kx+b, we get y=x.
If y=0, x=0.
Therefore, the line passes through the origin and is not a tangent.
Ans should be C
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Re: coordinate geometry [#permalink] New post 03 Sep 2008, 08:32
KASSALMD wrote:
If you consider both statements together:
k+b = 1; b=1-k; b^2 = (1-k)^2 = 1+k^2-2k
k^2+b^2 = 1; b^2= 1-k^2
Therefore, 1+k^2-2k = 1-k^2
On solving we get,
k=1
If k=1, b=0
Substituting these values in the equation y= kx+b, we get y=x.
If y=0, x=0.
Therefore, the line passes through the origin and is not a tangent.
Ans should be C


you forgot the other solution when k=0 b=1
y=1.. which is tangent to the circle.. (See Walker post above)

so two solutions... insuffient.

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Re: coordinate geometry [#permalink] New post 03 Sep 2008, 09:48
Good Q and good answer
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Re: coordinate geometry [#permalink] New post 04 Sep 2008, 04:03
arjtryarjtry wrote:
Is line y = kx + b tangent to circle x^2 + y^2 = 1 ?

1. k + b = 1
2. k^2 + b^2 = 1


nice explanation Mr. Walker!
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Re: coordinate geometry   [#permalink] 04 Sep 2008, 04:03
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