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17 Aug 2008, 15:36
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Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?
1) x intercept of k is greater than 1.
2) slope of k is -1/10.
Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.
OA is E.
My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.
1) x intercept of k is greater than 1.
2) slope of k is -1/10.
Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.
OA is E.
My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.
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17 Aug 2008, 16:15
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bhushangiri
You can do this one w/o doing any math. Just visualize a circle in the coordinate plane with center (0,0) and radius 1
(1) Insufficient
If the x intercept is greater than 1, there are lines that don't intersect the circle (e.g., a vertical line). There are lines that do (e.g., lines with very small negative slopes will intercept the top half of the circle)
(2) Slope if -1/10
As long as the x-intercept is sufficiently far away (e.g., at (1000000,0)), this line won't intersect the circle.
(1) and (2)
See explanation for (2)
17 Aug 2008, 16:18
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bhushangiri
You're think about it wrong here. In the vicinity of 1, a line of slope -1/10 will intersect, but the problem doesn't say vicinity, it just says greater than.
