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DS Geometry Prob

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DS Geometry Prob

by asbestos » Sun Jun 07, 2009 1:42 am
A line's slope is M and its intercept on the axis-y is N. In the same plane, there is a circle, which centre is origin and the radius is R. How many intercepts does the line have with the circle?
1) R^2<M^2
2) R^2<N^2
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Source: — Data Sufficiency |
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by yogami » Sun Jun 07, 2009 6:02 am
I could be wrong but I am getting an (E)


From (1) I am getting M > R and M > -R. Lets say for simplicity this wasn't a line which was parallel to either axis then (1) means that the ratio of the difference of y co-ordinates to the x co-ordinates of the line intersecting at the Y and X axis is greater than R. There could be infinite lines like these. Some intersect and some do not intersect the circle. I am visualizing this as I type because I can't think of a mathematically proper way to explain this.
So Insufficient
From (2) I am getting N > R and N > -R. This is easy to visualize. I mean we know that the point N is above the circle on Y axis. But the line may or may not intersect the circle. So insufficient.
Combining 1 and 2 we still get nothing

Hence (E)
200 or 800. It don't matter no more.
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