Question regarding the Asymptotes of HyperbolaTake 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?

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Question regarding the Asymptotes of HyperbolaTake 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?

Andre Reynolds · Accepted Answer

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 &quot;at infinity&quot;, that is,   z  =  0.

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.

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