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  • Help me please, - Limit , continuity and differentiability - JEE Main-3

If the curves y^2=6x, 9x^2+by^2=16,  intersect each other at right angles, then the value of b is :

  • Option 1)

    9/2

  • Option 2)

    6

  • Option 3)

    7/2

  • Option 4)

    4

 

Answers (1)

best_answer

As we learnt in

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.

 

Condition of Orthogonality -

Two curves intersect each other orthogonally if the tangents to each of them subtend a right angle at the point of intersection of two curves:

m_{1}\times m_{2}=-1

 

for C_{1}; 2yy' =6\Rightarrow y'=3/y=m_{1}

for C_{2}; 2yy' = 18x+2yy'=0\Rightarrow y' = \frac{-9x}{by}=m_{2}

so m_{1}m_{2}= -1

\frac{3}{y}\times \frac{-9x}{by}=-1

\Rightarrow by^{2}= 27x

\Rightarrow b\times 6x= 27x \Rightarrow b=9/2

 

-

 

 


Option 1)

9/2

Option 2)

6

Option 3)

7/2

Option 4)

4

Posted by

Himanshu

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