anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
the point \((m,n)\)?
anonymous
  • anonymous
I used implicit diff. to get y' = (2a^2y)/(2b^2x) but then what's next?
anonymous
  • anonymous
Yes the point (m, n)

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More answers

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

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