Find the equation of the tangent line to the hyperbola at the given point: (x^2/a^2) - (y^2/b^2) = 1 (m, n) and write your answer in the form y=f(x) for some function f(x).

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Find the equation of the tangent line to the hyperbola at the given point: (x^2/a^2) - (y^2/b^2) = 1 (m, n) and write your answer in the form y=f(x) for some function f(x).

Mathematics
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the point \((m,n)\)?
I used implicit diff. to get y' = (2a^2y)/(2b^2x) but then what's next?
Yes the point (m, n)

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Other answers:

cancel the twos
Yup
replace \(x\) by \(m\) and \(y\) my \(n\) for your slope
so a^2y / b^2x becomes a^2n / b^2m ?
yeah
then use the point - slope formula
So, y = (a^2n / b^2m)(x-m) + n ?
yeah, nice and ugly
i actually didn't check your derivative but i assume it is right
hmm maybe it is not
Yeah its not... >.<
shouldn't it be \[\frac{b^2x}{a^2y}\]?
I still get the wrong answer with that
you still need to replace m and n for x and y
\[\frac{b^2m}{b^2n}(x-m)+n\] try that
put an a^2 on bottom there instead of that b^2 :p
it is late
yes I know it is time for the old folks to retire
that includes me of course
((b^2m) / (a^2n))(x-m) + n thats right
:D Thanks so much!! @satellite73 @freckles :D
yw
I'm just satellite's cheerleader on this one! Go satellite!!!
And Tracy! :)
Ahaha XD thats an important role @freckles !!

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