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# Circle C and line K lie in the XY plane. If circle C is

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Circle C and line K lie in the XY plane. If circle C is [#permalink]

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28 Apr 2010, 07:41
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Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.
[Reveal] Spoiler: OA
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Re: Does line K intersect circle C? [#permalink]

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28 Apr 2010, 07:59
zz0vlb wrote:
Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.

[Reveal] Spoiler:
E

Let the line is $$y -mx +c =0$$

Now if the distance from the center of circle > radius => Line lie outside circle and does intersect with the line.

Distance = $$\frac{|y1-mx1+c|}{\sqrt{(1+m^2)}}$$

Distance from (0,0) = $$\frac{|0*1-m*0+c|}{\sqrt{(1+m^2)}}$$
= $$\frac{|c|}{\sqrt{(1+m^2)}}$$

Since it depends upon both c and m , thus both the statements individually are not sufficient.
So rule out A B and D

Now take 2nd equation m = -1/10

Distance becomes =$$|c|/\sqrt{{1+\frac{1}{10}^2}}$$

d = $$|c|*\sqrt{\frac{100}{101}}$$

Now c>1, but still we cannot say anything about d as if c > $$\sqrt{\frac{101}{100}}$$.
then d>1 else d<1 ( take the case when $$\sqrt{\frac{101}{100}}$$ $$> c > 1$$

thus E
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Re: Does line K intersect circle C? [#permalink]

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28 Apr 2010, 08:38
zz0vlb wrote:
Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.

[Reveal] Spoiler:
E

No matter what the slope is, it’s possible for line not to cross the circle as the x intercept can be + infinite.

(1) Just says that x intercept is right to the circle. Not sufficient
(2) Just says that slope is -1/10 --> line is just going down. Not sufficient.

(1)+(2) As we don't know exact intercept of line and X-axis we can not determine whether line intersects the circle or not. Not sufficient.

To elaborate more: we can draw infinitely many parallel lines with X-intercept more than 1 and slope -1/10, some will intersect the circle and some not.

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22 Aug 2010, 18:53
I understand this one a little bit but I'd like some more clarity. As far as statement 2 goes, other than the fact that the slope is negative, what else can I gather from it. Thanks

Circle C and line k lie in the xy-plane. If circle C is centered at the origin and has radius 1, does line k intersect circle C?

(1) The x-intercept of line k is greater than 1
(2) The slope of line k is -1/10
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Re: Does line K intersect circle C? [#permalink]

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31 Aug 2010, 23:03
Good explanation by the master!!
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Re: Does line K intersect circle C? [#permalink]

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01 Sep 2010, 09:41
+1 E

The line may be under the circle and very far. It will never touch the circle.

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Re: Does line K intersect circle C?   [#permalink] 01 Sep 2010, 09:41
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