Circle C and line K lie in the xy plane.

[anoo.anand]

I have a tough time with questions on co-ordinate geometry because I dont know what to look for in the question..pls help!!


This one is from GMAT Prep

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

what should be the approach in this case ?

equation or diagram...

another question is it says line K ... can we interpret it as since we do not know that the line is finitie or infinite...thus answer is E ??

[andrew]

I would approach this as a diagram...

just draw a circle with the center at 0,0... with a radius of 1 the circle will touch (0,1) (1,0) (0,-1) & (-1,0)

Statement (1) tells you that line K (and i'm pretty sure that yes you imagine it's infinite because it would be called line segment k something not line k) has an x-intercept greater than 1... on your diagram this would be to the right of the point (1,0) you have the circle touching... since you have no idea how far right this point is, it could be at (5000,0) or (2,0) and you have no idea what the slope is, it could be a vertical line like x=5000 or x=2 and never touch the circle, or a regular positive or negative slope. Not sufficient

Statement (2) tells you that the slope of line k is -1/10... this tells you absolutley nothing about the placement of the line in relation of the circle... not sufficient

Together imagine the two examples I gave for possible places of line k on the x-axis... If line K's x-intercept was at (2,0) with a slope of -1/10 it would run right into the circle as it is 1 unit away and hit the y-axis at (0,1/5) (in the circle)... now imagine the line K hits the x-axis at (5000,0) all the way to the right of the circle with a slope of -1/10 it would run all the way back to the y-axis and touch it at (0,500) way above the circle...

therefore the answer is E

when I get questions like these I look for restraints... if there are none I try to use extreme examples!!! if it said the x-intercept was between 1 and 5, I would have no choice but to test 1 and 5... since it says greater than 1, I take that as a hint to use extreme examples...


Hope this helps

[nitin_prakash_khanna]

Original Poster.

To answer your question.
another question is it says line K ... can we interpret it as since we do not know that the line is finitie or infinite...thus answer is E ??


A line is ialways infinite i.e extends from negative infinity to positive infinity.
Finite Line is called segment.

[anoo.anand]

thanks... to both of you.

[RonPurewal]

i wrote a whole book about this problem here

post18830.html#p18830