If tangent lines to the hyperbola $9x^2-y^2=36 \;$ intersect y-axis at point $(0,6)$, find the points of tangency.
How to find points of tangency on a hyperbola?
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calculus
geometry
conic-sections
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0The ([hyperbolic-geometry](http://en.wikipedia.org/wiki/Hyperbolic_geometry)) tag does not mean "involves hyperbolas." :) – 2011-10-16
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0i hope this help you http://www.youtube.com/watch?v=c_8QQbVQKU0 – 2011-10-16
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5This question is similar to the other question you asked. What have you tried so far in solving this one? – 2011-10-16
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0You 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): – 2011-10-16
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0I solved this question instantly. I'm just a little bit confused about its geometric representation. In which quadrants would points of tangency lie? – 2011-10-16
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0Can anyone give me the final answer? I know the intermediate steps. I just want a verification of what I have done. – 2011-10-16
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3@Muavia: You want a verification of what you've done without telling us what you've done? – 2011-10-16
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0Indeed, 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
1 Answers
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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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0great @pedja ,great answer – 2011-10-16