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This question already has an answer here:

Suppose that the conditions which ensure that the following equation is an hyperbola are verified:

$$ax^2+2bxy+cy^2+2dx+2ey+f=0$$

What are the general expressions of the two asymptotes of the hyperbola?


EDIT

I tried to follow the procedure here, but I get (I assumed all the coefficient greater than zero; if I did not give a sign to the coefficients, I cannot solve the limit):

$$\lim_{x \rightarrow + \infty} y(x) - mx = $$

$$ = \lim_{x \rightarrow + \infty} \frac{-E- Cx + \sqrt{(E + Cx)^2 - 4B(Dx + F)}}{2B} - \frac{2A}{C}x = - \infty$$

Thank you for your help.

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marked as duplicate by Andrei, YiFan, mrtaurho, José Carlos Santos, Aretino geometry May 12 at 21:07

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ See also the other answer of the duplicate question. $\endgroup$ – Aretino May 12 at 21:11
  • $\begingroup$ Hello @Aretino, the answer of Ng Chung Tak? $\endgroup$ – Gennaro Arguzzi May 13 at 7:32
  • $\begingroup$ Yes, exactly: that's simpler to use. $\endgroup$ – Aretino May 13 at 7:35
  • $\begingroup$ @Aretino Please see my comment to Ng Chung Tak. $\endgroup$ – Gennaro Arguzzi May 13 at 9:17