# How to find points of tangency on a hyperbola?

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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The (hyperbolic-geometry) tag does not mean "involves hyperbolas." :) – anon Oct 16 '11 at 9:40
This question is similar to the other question you asked. What have you tried so far in solving this one? – yunone Oct 16 '11 at 9:44
You do in the very same way I explained to you in the ellipse problem. The method works in principle for every plane algebraic curve and is very effective in the case of conics (where it reduces to an elementary question about quadratic equations): – Andrea Mori Oct 16 '11 at 9:49
@Muavia: You want a verification of what you've done without telling us what you've done? – anon Oct 16 '11 at 10:22

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 answer – dato datuashvili Oct 16 '11 at 9:59