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k intersect circle C

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k intersect circle C

by sanju09 » Wed Apr 08, 2009 3:37 am
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.


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by bluementor » Wed Apr 08, 2009 7:57 am
Let's say:

b = x intercept
c = y intercept

Statement 1:

b>1
if c>1, then line k does not intersect the circle (depending on how large b is)
if -1<c<1, then line k will intersect the circle. Insufficient.

Statement 2:

slope = -1/10.

without the knowledge of known point on line k, it is impossible to know if this line intersects the circle. Insufficient.

Both statements together:

slope = -c/b
-1/10 = -c/b
b = 10c

since b>1, then:
10c>1
c>1/10

if c is less than 1, then the line definitely intersects the circle. if c is much larger than 1, then the line does not intersect the circle. Insufficient.

Choose E.

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