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
How do u solve this? My geo is pathetic
Geo - Gmat prep
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 103
- Joined: Wed May 30, 2007 6:17 am
- Followed by:1 members
My answer would be [E]. I know the equation of the circle here istanyajoseph wrote: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
How do u solve this? My geo is pathetic
x^2 + y^2 = 1 .......... (a)
... and the equation of the line from (2) is
y = (-1/10)x + b ............. (b)
I don't really know how to proceed any further. Not sure if any one pair of (x, y) will satisfy both the equations. If there is a way to mathematically determine that, I'll be very interested in knowing.
I think the fact that 'b' is a unknown variable is causing me to choose [E] at this point.
What is the OA and explanation?
-
- Master | Next Rank: 500 Posts
- Posts: 103
- Joined: Wed May 30, 2007 6:17 am
- Followed by:1 members
This question is pretty easy if you just think about it conceptually.
It tells you that the X-intercept is greater than 1... this doesn't tell you anything. Imagine that the X-intercept is 1 million. You would near a near-0 slope for the line to intersect the circle. A slope of -1/10 would definitely not intersect the circle. Now imagine that the X-intercept is 1.000000001. With a slope of -1/10, the line will definitely intersect the circle in the upper right quadrant.
It tells you that the X-intercept is greater than 1... this doesn't tell you anything. Imagine that the X-intercept is 1 million. You would near a near-0 slope for the line to intersect the circle. A slope of -1/10 would definitely not intersect the circle. Now imagine that the X-intercept is 1.000000001. With a slope of -1/10, the line will definitely intersect the circle in the upper right quadrant.