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Geo - Gmat prep

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by tanyajoseph » Thu Aug 09, 2007 12:16 pm
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

How do u solve this? My geo is pathetic :(
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Re: Geo - Gmat prep

by bingojohn » Fri Aug 10, 2007 8:00 am
tanyajoseph 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

How do u solve this? My geo is pathetic :(
My answer would be [E]. I know the equation of the circle here is

x^2 + y^2 = 1 .......... (a)

... and the equation of the line from (2) is

y = (-1/10)x + b ............. (b)

I don't really know how to proceed any further. Not sure if any one pair of (x, y) will satisfy both the equations. If there is a way to mathematically determine that, I'll be very interested in knowing.

I think the fact that 'b' is a unknown variable is causing me to choose [E] at this point.

What is the OA and explanation?
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by tanyajoseph » Sat Aug 11, 2007 7:23 am
This is the GMAT prep q and so no explanation. However u got the answer right - its E
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by beny » Sat Aug 11, 2007 8:56 pm
This question is pretty easy if you just think about it conceptually.

It tells you that the X-intercept is greater than 1... this doesn't tell you anything. Imagine that the X-intercept is 1 million. You would near a near-0 slope for the line to intersect the circle. A slope of -1/10 would definitely not intersect the circle. Now imagine that the X-intercept is 1.000000001. With a slope of -1/10, the line will definitely intersect the circle in the upper right quadrant.
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