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If tangent lines to the hyperbola $9x^2-y^2=36 \;$ intersect y-axis at point $(0,6)$, find the points of tangency.

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    Indeed, that isn't quite fair. If you don't show what you did, we can't be that helpful in showing what you're doing right, and otherwise...2011-10-16

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Write hyperbola as:

$\frac{x^2}{4}-\frac{y^2}{36}=1$ , then solve system:

$\begin{cases} y_0=kx_0+n \\ n^2=a^2k^2-b^2 \end{cases}$

where $x_0=0 , y_0=6 ,a^2=4 ,b^2=36$

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    great @pedja ,great answer2011-10-16