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 .