Question

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).

Answer 1

the point \((m,n)\)?

Answer 2

I used implicit diff. to get

y' = (2a^2y)/(2b^2x)

but then what's next?

Answer 3

Yes the point (m, n)

Answer 4

cancel the twos

Answer 5

Yup

Answer 6

replace \(x\) by \(m\) and \(y\) my \(n\) for your slope

Answer 7

so a^2y / b^2x becomes a^2n / b^2m ?

Answer 8

yeah

Answer 9

then use the point - slope formula

Answer 10

So, y = (a^2n / b^2m)(x-m) + n ?

Answer 11

yeah, nice and ugly

Answer 12

i actually didn't check your derivative but i assume it is right

Answer 13

hmm maybe it is not

Answer 14

Yeah its not... >.<

Answer 15

shouldn't it be
\[\frac{b^2x}{a^2y}\]?

Answer 16

I still get the wrong answer with that

Answer 17

you still need to replace m and n for x and y

Answer 18

\[\frac{b^2m}{b^2n}(x-m)+n\] try that

Answer 19

put an a^2 on bottom there instead of that b^2 :p

Answer 20

it is late

Answer 21

yes I know
it is time for the old folks to retire

Answer 22

that includes me of course

Answer 23

((b^2m) / (a^2n))(x-m) + n

thats right

Answer 24

:D Thanks so much!! @satellite73 @freckles :D

Answer 25

yw

Answer 26

I'm just satellite's cheerleader on this one!
Go satellite!!!

Answer 27

And Tracy! :)

Answer 28

Ahaha XD thats an important role @freckles !!