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VS: value of S

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Manager
Joined: 22 Sep 2008
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05 Oct 2008, 03:37
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Intern
Joined: 04 Oct 2008
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Re: VS: value of S [#permalink]

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05 Oct 2008, 08:25

$$(-sqrt3,1)$$ is not on the unit circle, but $$((-sqrt3)/2,1/2)$$ is.

This leads me to believe that point P lies on the circle with radius 2 at 150 degrees.

150 - 90 = 60

2*(cos 60) = 1

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SVP
Joined: 17 Jun 2008
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Re: VS: value of S [#permalink]

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05 Oct 2008, 12:45
Since OP and OQ are perpendicular to each other, multiplication of their slopes will be -1.

Or. (t/s)(1/-sqrt3) = -1 or t = (sqrt3)s.

Also, equation of circle with radius 2 is x^2 + y^2 = 4 and since, (s,t) lies on circle, hence s^2 + t^2 = 4 or s^2 + 3s^2 = 4 or s = 1 (as -1 is not the answer choice )

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Senior Manager
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Re: VS: value of S [#permalink]

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05 Oct 2008, 13:31

Solve this using pythagorean theorem to find P's distance from x and y intersection
distance^2=sqrt3+2= 2

Q must be equidistant and therefore 2

using 90 triangle rule calculate the hypothenus 2, 2 so 2*sqrt2

subtract sqrt3

and you get 1.096 as a solution!
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Last edited by spiridon on 06 Oct 2008, 08:14, edited 2 times in total.

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Manager
Joined: 30 Sep 2008
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Re: VS: value of S [#permalink]

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05 Oct 2008, 23:43
csvobo wrote:

$$(-sqrt3,1)$$ is not on the unit circle, but $$((-sqrt3)/2,1/2)$$ is.

This leads me to believe that point P lies on the circle with radius 2 at 150 degrees.

150 - 90 = 60

2*(cos 60) = 1

good approach

Call <PO(-x) = <O1
<QOx = <O2

tanO1 = sqrt(3) / 1 => <O1 = 30' => <O2 = 60'

OP = OQ = sqrt (sqrt(3)^2 + 1) = 2

s = cos60 x OQ = 1/2 * 2 = 1

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Manager
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Re: VS: value of S [#permalink]

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06 Oct 2008, 06:00
Hey how you guys come to know radius is '2'?

Thanks

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Director
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WE 1: Investment Banking - 6yrs
Re: VS: value of S [#permalink]

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06 Oct 2008, 06:56
Left to Right - co-ordinates shift
Top to Down - Signs shift

Also, you know the signs for the below
I = a>0,b>0
II = a<0,b>0
III = a<0,b<0
IV = a<0,b<0

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Manager
Joined: 22 Sep 2008
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Re: VS: value of S [#permalink]

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08 Oct 2008, 20:28
sorry guys.. me not expert in maths..

how to do you derive this thing "This leads me to believe that point P lies on the circle with radius 2 at 150 degrees."

3/4 +1/4 =1 i understand till this point.. unit circle. but not more that that.

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Re: VS: value of S   [#permalink] 08 Oct 2008, 20:28
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