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# Circle C and line K lie in xy-plane. If circle C is centered

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Senior Manager
Joined: 05 Aug 2005
Posts: 410
Circle C and line K lie in xy-plane. If circle C is centered [#permalink]

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15 Sep 2006, 16:58
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Circle C and line K lie in 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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Joined: 02 Jun 2006
Posts: 1260

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15 Sep 2006, 17:37

S1: X-intercept > 1

For any line y = mx + c, @ y= 0, x > 1
i.e. -c/m > 1

Cases :
c > 0, m < 0 OR
c < 0, m > 0

Not sufficient.

S2: Slope m = -1/10

Eqn of line : y = -x/10 + C
If y = 0 , x = 10C

C could be anything ..

Not sufficient.

S1 & S2:

x intercept > 1, m = -1/10

y = -x/10 + C

@ y = 0,

x =10C

Given x > 1
or 10C > 1
or C > 1/10

If x = 0, y = C y could be 1/20 or 20
Given x > 1, x could be 1/10 or 10

If (x, y) = (1/20, 1/10) Line intersects
If (x, y) = (10, 20) line does not.

Not sufficient.

15 Sep 2006, 17:37
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