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Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink]

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26 Mar 2009, 13:06

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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.

Re: Circle C and line K lie in the XY plane. If circle C is centered at th [#permalink]

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02 Oct 2014, 00:53

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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.