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I must describe the conditions in which an infinite continuous line (ax+by=c) will only cross a parabola once. I believe the only answer is a straight, vertical line because while the slope of the parabola may approach zero and become extremely small it will never be zero. Therefore if the line has any slope at all, not matter how small, it will eventually cross the parabola again.

Am I correct in this conclusion? Are there options besides a vertical line?

Thanking you in advance,

Linus