There wasn't a mistake, just one more step was needed:
Is there a method to do this division, and how do you get the intuition to divide it anyway? o_O
I am simultaneously solving
1) The equation of the hyperbola ##y-y_{1}=\frac{b^{2} x_{1}}{a^{2} y_{1}}\left(x-x_{1}\right)## with the equation of the top asymptote ## bx + ay = 0##
2) The equation of the hyperbola ##y-y_{1}=\frac{b^{2} x_{1}}{a^{2} y_{1}}\left(x-x_{1}\right)## with the...
Summary:: Question: Show that the segment of a tangent to a hyperbola which lies between the asymptotes is bisected at the point of tangency.
From what I understand of the solution, I should be getting two values of x for the intersection that should be equivalent but with different signs...
I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T?
Answer: I just can seem to get to this. I think I'm there but can't get it in...