Asymptotes

 


 How to determine the asymptote or asymptotes :-

-----  In order to obtain the asymptotes parallel to the axis of  x,

equate to zero the co-efficient of the highest power of   x.

For example, if the curve be in the   n th  degree

and the term containing   n th power of   x    be absent,

then the co-efficient of   (n-1) the power of  x   equated to zero

will give the asymptotes parallel to the axis of   x.

-----  If both the terms containing    n th power of  x   and

(n-1) th power of  x  be absent, then the co-efficient of

(n-2) th power of  x   equated to zero will give two asymptotes

parallel to the axis of   x.

-----  To get the asymptotes parallel to the axis of  y,

equate to zero the co-efficient of the highest power of   y.

For example, if the curve be the   n th   degree and

the term containing  n th power of  y  be absent,

then the co-efficient of   (n-1) th power of  y equated to zero

will give the asymptotes parallel to the axis of  y.

-----  If both the terms containing   n th power of  y and

(n-1) th power of  y  be absent, then the co-efficient of

(n-2) th power of  y  equated to zero will give two asymptotes

parallel to the axis of  y.