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In the xy-plane, does the line L intersect the graph of y = x^2
I. Line L passes through (4, -8)
II. Line L passes through (-4, 16)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Option B is the correct answer.
y=x^2 is a parabola with vertex at (0,0) and upward……
Statement I is insufficient: Line passes through (4,-8); if the line is parallel to X-axis it can never intersect the parabola…. if the line is parallel to Y-axis it will… Not Sufficient
Statement II is sufficient: Line passes through (-4,16); observe that this point is on y=x^2 which means the line is intersecting parabola at the point…. It may or may not intersect y=x^2 at some other point, we don’t bother about it…. because the question asks for if the line is intersecting y=x^2 or not… so just a yes or no question…. in this case it is intersecting the graph… so sufficient….
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