1. Asymptotes: A St. live l is called an asymptote of an infinite branch of a curve iff perpendicular distance of a point p on that branch from the st. line l levels to zero as p moves to along the branch.

2. Rectangular Asymptote: If an asymptote of any curve is either parallel to x-axis or parallel to y-axis then it is called rectangular asymptote.

3. Oblique Asymptote: The asymptote of any curve neither parallel to x-axis nor parallel y-axis.

4. To find asymptotes parallel to y-axis
To find asymptotes parallel to y-axis. Rule 1:If the equation of the curve is of the form y=N(x)/D(x), where N(x) and D(x) are polynomials in x without any common factors and D(x)=0 gives x=c1,c2,c3………

5. Rule 2:If the equation of the curve can not be put in the from y=N(x)/D(x), then the vertical asymptotes are obtain by equating to zero the real linear factors in the co-efficient of the highest power of y in the equation of the given curve.

6. To find asymtote parallel to x-axis If the equation of the curve can not put in the form of x=N(y)/ D(y), then the Horizontal Asymptotes are obtained by equating to zero the linear factors in the equation of the given curve.

7. Questions:- 1.y=x(x-1)(x-2) 2.3xy+5x-4y-3=0

8. Oblique Asymptotes: A straight line L of inclination other then 0 or 90 is said to be oblique asymptote of the curve y=f(x) if the distance between the points p(x,f(x) and the straight line L approaches zero as x or-

9. If y=mx+c is an asymptote of the given curve,prove that

10. Procedure to find oblique asymptotes: 1
Procedure to find oblique asymptotes: 1. put x=1 and y=m in nth degree terms and (n-1)th degree terms and obtain

11. 2. Find all the real roots of 3
2.Find all the real roots of For every non repeated real root of corresponding value of c is given by

12. 4. For every repeated root of occurring twice corresponding value of c is given by

13. Questions: 1.Find all the asymptotes of the curves (i)(x+2y)(x-2y)(x-y)-2x(x-4y)+2x=0 (ii)

14. Intersection of a curve and its asymptotes: 1
Intersection of a curve and its asymptotes: 1. The n asymptote of a curve of nth degree cuts the curve in at the most n(n-2) points . 2. if the equation of the curve is of the form and the curve has no parallel asymptotes then the points of intersection of the curve and its asymptotes lie on

15. Questions: 1.show that the asymptotes of the curve cut the curve in atmost three points which lie on the curve 3x-y-1=0 2.Find the equation of the hyperbola having as its asymptotes and passing through origin.

16. Asymptotes of polar curve Theorem :Let the equation of the polar curve be expressed as Letbe the root of f()=0 Then is an asymptote of the curve

17. Questions: 1.rlog =a. 2.r=asec+btan