If tangent lines to the hyperbola $9x^2-y^2=36 \;$ intersect y-axis at point $(0,6)$, find the points of tangency.
2026-04-26 07:50:22.1777189822
How to find points of tangency on a hyperbola?
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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 $x_0=0 , y_0=6 ,a^2=4 ,b^2=36$