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  • I have a doubt, kindly clarify. - Limit , continuity and differentiability - JEE Main-12

The angle of inetersection between curves y^{2} = 4x and y^{2} = 5 - x is \theta then \tan\theta equals ?

  • Option 1)

    \frac{4}{3}

  • Option 2)

    \frac{5}{3}

  • Option 3)

    \frac{7}{3}

  • Option 4)

    \frac{8}{3}

 

Answers (1)

best_answer

As we have learned

Angle of intersection of two curves -

The angle of intersection of two curves is the angle subtended between the tangents at their point of intersection.Let  m1  &  m2 are two slope of tangents at intersection point of two curves then

tan\theta=\frac{[m_{1}-m_{2}]}{1+m_{1}m_{2}}

- wherein

where \theta is angle between two curves tangents.

 

 First of all we need point of intersection , solving together we get \rightarrow 4x=5-x\rightarrow x=1\therefore  points of intersection are (1,2),(1,-2) 

Because of symmetry , angles at both point will be same y^{2}=4x\Rightarrow 2y\frac{dy}{dx}=4 \Rightarrow \frac{dy}{dx}|_{(1,2)}=4/4=1; y^{2}=5-x\Rightarrow 2y\frac{dy}{dx}=-1

\Rightarrow \frac{dy}{dx}|_{(1,2)} =-1/4

\therefore \tan \theta = \left | \frac{1+1/4}{1-1/4} \right |=5/3

 

 

 

 

 


Option 1)

\frac{4}{3}

Option 2)

\frac{5}{3}

Option 3)

\frac{7}{3}

Option 4)

\frac{8}{3}

Posted by

Himanshu

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