Calculating the asymptotes of an hyperbola from the general equation

Asked May 12 '19 at 17:20

Active May 12 '19 at 19:41

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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.

edited May 12 '19 at 19:41

asked May 12 '19 at 17:20

Gennaro Arguzzi

1,150

See also the other answer of the duplicate question. – Intelligenti pauca May 12 '19 at 21:11
Hello @Aretino, the answer of Ng Chung Tak? – Gennaro Arguzzi May 13 '19 at 07:32
Yes, exactly: that's simpler to use. – Intelligenti pauca May 13 '19 at 07:35
@Aretino Please see my comment to Ng Chung Tak. – Gennaro Arguzzi May 13 '19 at 09:17

Calculating the asymptotes of an hyperbola from the general equation

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