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What is the least possible distance between a point on the c

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What is the least possible distance between a point on the c [#permalink]

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New post 21 Mar 2011, 21:40
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What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?

A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-least-possible-distance-between-a-point-on-the-92566.html
[Reveal] Spoiler: OA
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Re: co-ordinate geometry problem [#permalink]

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New post 21 Mar 2011, 21:53
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First plot the line. The y intercept is (0,-3) the x intercept is (4,0)
The height of the triangle formed by the triangle with vertices (0,0),(0,-3),(4,0) is say h. It's area is 1/2*3*4=6. the hyp of the triangle is 5 (triplet 3:4:5).
Therefore 1/2*h*5=6 hence h =12/5=2.4
Now the min distaff between the circle and line is 2.4-radius. Radius is 1. Hence min distance is 1.4. A is the answer
asmit123 wrote:
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?
A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0


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Re: co-ordinate geometry problem [#permalink]

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New post 21 Mar 2011, 22:32
Thanks friend. That was very clear.
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Re: co-ordinate geometry problem [#permalink]

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New post 22 Mar 2011, 01:14
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Re: co-ordinate geometry problem [#permalink]

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New post 22 Mar 2011, 02:52
Excellent explanation gmat1220.

+1 to you.
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Re: co-ordinate geometry problem [#permalink]

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New post 22 Mar 2011, 08:32
gmat1220 wrote:
First plot the line. The y intercept is (0,-3) the x intercept is (4,0)
The height of the triangle formed by the triangle with vertices (0,0),(0,-3),(4,0) is say h. It's area is 1/2*3*4=6. the hyp of the triangle is 5 (triplet 3:4:5).
Therefore 1/2*h*5=6 hence h =12/5=2.4
Now the min distaff between the circle and line is 2.4-radius. Radius is 1. Hence min distance is 1.4. A is the answer
asmit123 wrote:
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?
A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0


Posted from my mobile device

Good Post thanks gmat1220
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Re: co-ordinate geometry problem [#permalink]

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New post 11 Aug 2013, 10:07
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you can use the formula distance from a point (x", y") to a line ax+by+c is

|ax"+ by" +c |/ sqrt (a^2 + b ^2)

Here the equation of the circle x^2 + y^2 = 1 implies (x", y") = (0,0) and radius =1

Equation of the line y= 3/4 x- 3 writing it in ax+by+c=0 format 3/4x-y-3 = 0


| -3| / sqrt ( (3/4)^2 +1)

simplying you get 3 * 4/5
= 2.4

since radius is 1 distance from circle to line is 2.4 - 1 = 1.4
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Re: What is the least possible distance between a point on the c [#permalink]

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New post 11 Aug 2013, 10:10
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Re: What is the least possible distance between a point on the c [#permalink]

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New post 11 Aug 2013, 14:44
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Re: What is the least possible distance between a point on the c   [#permalink] 11 Aug 2013, 14:44
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