Angle Between Curves

Here is some Working Rule on Angle between Curves ;

1)  If Equations of two curves are given . Find the value of    dy/dx     fom the equation of two curves .

2)  If the value of     dy/dx    obtained from the two equations are equal then , angle between the curve is    0 degree    i.e. they touch each other at each point  i.e. the two curves are same .

If product of the values of     dy/dx     for two curves is    -1,   then the two curves cut each other orthogonally (perpendicularly) .

3)  If given condition (2) is not true , find the co-ordinates of the points of intersection of the two curves by solving the equation of the two curves .

Then find the values of     dy/dx    from the equation of two curves at one point of intersection .

This will give gradient of the tangent to the two curves
i.e.    m1     and    m2    .

Then find the angle     A       between the curves by the formula

tanA= +and- [m1 -m2]/1 + m1m2    .

Do this fo every point of intersection .