TARGET730 wrote:
Does the line L intersect the graph of the curve y = x^2 – 6?
(1) The line L passes through the origin and makes an angle of 45o with the positive x-axis.
(2) The line L passes through the point (-2, -2) and (2, 2).
Note here that all you need to worry about is getting a unique line. If you have the equation of a line and that of a curve, you will be able to say whether the line intersects the curve or not. The point is that it is not important to figure out whether it actually does intersect because in either case, the information will be sufficient - irrespective of whether the answer is yes or no. So actually drawing the curve and the line is not required.
Both statements individually give you a distinct line. So you will be able to say whether the line intersects the curve or not.
Answer (D)
This brings up an interesting question - given the equation of the curve y = x^2 – 6, what kind of lines will not intersect it? Think about it.
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Karishma
Veritas Prep GMAT Instructor
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