Prove all lines parallel to an asymptote of a hyperbola intersect the hyperbola once only – math.stackexchange.com

Prove all lines parallel to an asymptote of a hyperbola intersect the hyperbola once only – math.stackexchange.com

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A hyperbola has equation $\frac{x^2}{4}-\frac{y^2}{16}=1$. Show that every other line parallel to this asymptote, $y=2x$, intersects the hyperbola exactly once. So here's the hyperbola. The blue line ...

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