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tanyajoseph
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 Posted: Thu Aug 09, 2007 12:16 pm Post subject: Geo - Gmat prep |
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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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bingojohn
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| Posted: Fri Aug 10, 2007 8:00 am Post subject: Re: Geo - Gmat prep |
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| 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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tanyajoseph
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| Posted: Sat Aug 11, 2007 7:23 am Post subject: |
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| This is the GMAT prep q and so no explanation. However u got the answer right - its E |
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beny
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| Posted: Sat Aug 11, 2007 8:56 pm Post subject: |
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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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