Angle of intersection of two curves:

Let C₁: y= f(x) and C₂: y = g(x) be 2 curves. If 2 curves intersect at the point P (x₁, y₁). Then the angle of intersection of 2 curves can be defined as the angles between the tangents at their intersection. And can be given by

Note: 

(i) If curves touch at P, then q = 0 so that f ' (x₁) = g ' (x₁)

(ii) If the angle that is Two tangents are perpendicular to each other then the curves are said to cut orthogonally, then f '(x₁). g '(x₁) =- 1.

Illustration:   If curves x²-4y²+c=0 and y² = 4x intersect orthogonally then find range of c.

Solution: Curves will intersect if x² - 16 x + c = 0 has real roots. Therefore c £ 64.

                              For  

                              For  

                              If the curves intersect orthogonally then 

                  . But if y = 0, slope of both the curves undefined.

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