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

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Is line y=Kx + b tangent to circle x^2 + y^2 = 1? 1. k + b = [#permalink]  18 Dec 2007, 08:37
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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[#permalink]  18 Dec 2007, 09:15
E.

1. x² + y² = 1 - is a circle with the radius of 1 and with the center at x=0, y=0

2. (1;0) or (0,1) for (k;b) is satisfied both conditions.

3. for (1;0): y=kx. The line goes through the center and intersect the circle in two points: -1/√2, -1/√2 and 1/√2,1/√2, So, line does not tangent the circle.

4. for (0;1): y=1. The line tangents the circle in point 0,1.

Therefore, E
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[#permalink]  18 Dec 2007, 09:47
Thanks for the detailed explanation.
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[#permalink]  23 Dec 2007, 03:37
walker wrote:
E.

1. x² + y² = 1 - is a circle with the radius of 1 and with the center at x=0, y=0

2. (1;0) or (0,1) for (k;b) is satisfied both conditions.

3. for (1;0): y=kx. The line goes through the center and intersect the circle in two points: -1/√2, -1/√2 and 1/√2,1/√2, So, line does not tangent the circle.

4. for (0;1): y=1. The line tangents the circle in point 0,1.

Therefore, E

Walker,
Can you please elaborate your explanation in light of the conditions .? I am not able to follow the same .
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[#permalink]  23 Dec 2007, 04:04
dynamo wrote:
Can you please elaborate your explanation in light of the conditions .? I am not able to follow the same .

(1;0) and (0,1) for (k;b) is satisfied each conditions separately but do not let us answer the question.
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[#permalink]  23 Dec 2007, 16:54
C is my answer.

(1) k+b=1 then k=1-b so y=(1-b)x+b
If b=0 then y=x and line is no tangent. If b=1 then y=1 and line is tangent

(2) k^2+b^2=1 then k=sqrt(1-b^2) so y=x·sqrt(1-b^2)+b
If b=0 then y=x and line is no tangent. If b=1 then y=1 and line is tangent

(1)^(2) k=1-b and k^2=1-b^2 so 1+b^2-2b=1-b^2 therefore b^2=2b.
b can take two values: b=0 and b=2. If b=0 then line is not tangent. I b=2 then k=-1 and y=-x+2 and line is not tangent.

Therefore C is the answer.
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Re: tangent line [#permalink]  23 Dec 2007, 17:31
bmwhype2 wrote:
Is line y=Kx + b tangent to circle x^2 + y^2 = 1?

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

the given circle has center (0,0) and radius 1.

The distance of a line ax+by+c=0 from point (p,q) is given by:
(ap+bq+c)/sqrt(a^2+b^2)

Here, we need to find the distance of the given line from point (0,0) and check if that distance is 1.

I get E as the answer.
Re: tangent line   [#permalink] 23 Dec 2007, 17:31
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