Question regarding the Asymptotes of Hyperbola Is it possible that the graph of function has infinitely many vertical asymptotes? I suppose, that it is not possible, because such function would not exist. But I need to prove it in a math-fashioned-way, and I'm clueless how to do it.

Dillan Valenzuela

Dillan Valenzuela

Answered question

2022-08-11

Question regarding the Asymptotes of Hyperbola
Take a curve ,some curve which converges to a point as one variable( say x)tends to
lim x
,the value that it approaches (or) converges to ( y value) ,is the value of the asymptote ,the value that the curve tries to reach(y reluctantly tries to get to )but never reaches (or) only reaches the value at .
Now the equation of Hyperbola is given by
y ² b ²
To find the asymptotes we substitute y ² b ²
Why do we do that ?
What is happening here?
Is there any geometrical reasoning for this?
To find the asymptotes we take the RHS of the equation as 0,why so?

Answer & Explanation

Andre Reynolds

Andre Reynolds

Beginner2022-08-12Added 10 answers

The reason is that the projective equation (in homogeneous coordinates) of your hyperbola is
x 2 a 2 y 2 b 2 = z 2
and the asymptotes correspond with the points "at infinity", that is, z = 0.

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