It's known that the asymptotes of a hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is given by $y=\pm\frac{b}{a}x$ if $a>b$.
I tried to find a proof of the fact that why the equations of these asymptotes are like that,however the only reference (Thomas calculus book) that I found explained that the two asymptotes are derived by letting $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=0$.
As usual the book does not give a reason for that , (Well it's not surprising to see that the author of these elementary books always try to fill their book with every subjects consisting in mathematical without any kind of logical reason.these days publishing an elementary mathematics book is easy-peasy and the responsibility is completely lost ,as Galois says: "Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing difficulties.")
It would be highly appreciated if someone prove why the equation of the asymptotes have such form.
from Hot Weekly Questions - Mathematics Stack Exchange
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