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Circle C and Line K in the xy plane

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Circle C and Line K in the xy plane

by queenisabella » Sat Mar 31, 2012 6:10 pm
please help explain answer

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.

Answer is E..
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by Bill@VeritasPrep » Sat Mar 31, 2012 6:22 pm
If the radius of the circle is 1, then the equation for Circle C is x^2 + y^2 = 1, giving us intercepts at (0,1) (0,-1), (1,0), and (-1, 0).

1) We can come up with equations that will and will not intersect the circle. For example, y=-x + 1 will intersect the circle, while y=-x + 4 will not. Insufficient.

2) Again, we can come up with lines that will and will not intersect the circle. Y=(-1/10)x - 20 will not, while Y=(-1/10)x + 1 will.

When combined, we run into the same problems. Y=(-1/10)x + 1 meets both requirements (it has an x-intercept of 10) and intersects the circle, while Y=(-1/10)x + 2 meets both and does not intersect the circle.
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by Anurag@Gurome » Sun Apr 01, 2012 9:37 pm
queenisabella wrote:please help explain answer

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.

Answer is E..
(1) The x-intercept of line K is greater than 1 implies that the x-intercept of line K is towards the right of circle C but this does not imply if line K intersects circle C; NOT sufficient.

(2) The slope of line K is -1/10 implies line K goes down left to right, but again this does not imply if line K intersects circle C; NOT sufficient.

Combining (1) and (2), we do not know the exact intercept of line K, and we cannot find if line K intersects circle C or not; NOT sufficient.

The correct answer is E.
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by GMATGuruNY » Mon Apr 02, 2012 5:36 am
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