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Two curves touch each other if the angle between the tangents to the curves at the point of intersection is 0 o , in which case we will have, tanΨ 1 = tanΨ 2 .


Two curves touch each other if the angle between the tangents to the curves at the point of intersection is 0o, in which case we will have,


                 tanΨ1 = tanΨ2.


Grade:12th Pass

1 Answers

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
9 years ago

Hello sandeep !

 

First of all i would franky say that i didn't understand what to find or prove in the question ...

 

Angle between curves can be simply calculated by differentiating the function of curve ...!

 

Suppose two curves are there with equation f1(x) and f2(x)

 

df1(x)/dx will give the slope of tangent at f1(x)  and df2(x)/dx will give the slope of tangent at f2(x)

 

Suppose angle of tangent at f1(x) is  A and at f2(x) is B ..

 

then tan(A) - tan(B) = df1(x)/dx - df2(x)/dx

 

tan(A-B).[1 + tanA.tanB] = df1(x)/dx - df2(x)/dx   ( tan(A-B) = (tanA - tanB)/(1+tanA.tanB)

 

Hence if the angle between the curve is zero ...that is ...A-B = 0

 

So ...tan(A) = tan(B)    

 

Regards

 

Yagya

 

askiitians_expert

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