alex.gellatly 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 - .
Thanks
(1) If the x-intercept of line k is greater than 1, then it may or may not intersect the circle of radius 1 whose center is at origin, depending upon its inclination about the x-axis. For example, if line k is perpendicular to x-axis, then it would never intersect the given circle, and if its inclination is such that its y-intercept is between -1 and 1, or likewise, then the line k would intersect the given circle. Insufficient
(2) A negative slope only confirms that the inclination of line k with the positive x-axis is an obtuse angle. In the absence of x and y intercepts, nothing can be told about the intersection. Insufficient
Taking together,
we still cannot say that the line k would intersect the given circle or not, as x and y intercepts of line k could be any number greater than 1, big enough that it could not intersect the given circle, or the y-intercept suitably so small a positive number that it intersects. [spoiler]
Insufficient
Take E
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