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Circle C and line K lie in the XY plane. If circle C is centered at th

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Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 26 Mar 2009, 11:49
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51% (02:22) correct 49% (00:46) wrong based on 59 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: circle-c-and-line-k-lie-in-the-xy-plane-if-circle-c-is-101471.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Oct 2014, 02:21, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 26 Mar 2009, 12:06
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1. The x-intercept of line k is greater than 1.

We know the x-intercept but the slope of the line is not known. If line k has a very small slope and intersects the x-axis at 2,3,4..the line will intersect the circle and if the x-intercept is a relatively large number with a high slope, it will not intersect the circle...So statement 1 is insufficient.

2. The slope of line k is -1/10

Again, we know the slope, but we dont know where it intersects the x-axis. We know that we have a relatively flat line..so if it intersects the x-axis at 2,3,4,5..10 , it will intersect the circle but if it intersects the x-axis at 50,100,200 , it will not intersect the circle..So statement 2 is insufficient.

We are down to C and E.

Together, we again dont have sufficient info.
Let's take an example
Slope=-1/10 , x-axis intersection at (4,0)
y-y1=m(x-x1)
y=-0.1x+0.4...this line will intersect the y-axis at 0.4 ( hence intersect circle)

take another example
slope=-1/10, x-axis intersection at (100,0)
y=-0.1x+10 ..this line will intersect the y-axis at 10 ( hence NOT intersect the circle)...So it is insufficient.

Answer is E
What's the OA?
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 26 Mar 2009, 12:12
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let equation of the line k be
y = mx + b

1. The x-intercept of line k is greater than 1.
- it can be 1.5 or 100 , does not specify anything specific , INSUFFICIENT.

2. The slope of line k is -1/10
so ,
y = -x/10 + b
still , INSUFFICIENT as no information has been mentioned regarding x.

using both together,
y = -x/10 + b
still , INSUFFICIENT as b varies with x and may or may not be less than 1.

Answer : E
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 26 Mar 2009, 14:34
Perfect Guys.... OA is E
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 01 Oct 2014, 23:53
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink] New post 02 Oct 2014, 02:22
Expert's post
nitindas wrote:
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: circle-c-and-line-k-lie-in-the-xy-plane-if-circle-c-is-101471.html


Circle C and line K lie in the XY plane. If circle C is centered at the origin and has a radius 1, does line K intersect circle C?

The best way to solve this question would be to visualize/draw it.

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

(1) The X-Intercept of line k is greater than 1 --> Just says that X-intercept is to the right of the circle. Not sufficient
(2) The slope of line k is -1/10 --> Just says that slope is negative -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 (for example line with X-intercept 1.1) and some not (for example line with X-intercept 1,000,000). Check the image below for two possible scenarios: blue line (with the slope of -1/10 and the x-Intercept greater than 1) intersects the circle while the red line (also with the slope of -1/10 and the x-Intercept greater than 1) does not.
Image

Answer: E.

For more on this issue check Coordinate Geometry Chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: Circle C and line K lie in the XY plane. If circle C is centered at th   [#permalink] 02 Oct 2014, 02:22
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