In the xy-plane, does the line L intersect the graph of y = x^2

[BTGmoderatorDC]

In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)


OA B

Source: GMAT Prep

[swerve]

In the xy-plane, does the line L intersect the graph of y = x^2

(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)


OA B

Source: GMAT Prep

1) This is clearly insufficient. It is possible that the line might intersect the curve at \((4,16)\) ( if it has slope 0, like \(x=4\)), or might not intersect at all, like line \(y=-8.\)

2) This is sufficient as the line satisfies the equation of the curve \(y=x^2, 16=(-4)^2,\) therefore the line and curve intersect at this point.

Hence, B