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  • Need clarity, kindly explain! - Limit , continuity and differentiability - JEE Main-9

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

  • Option 1)

    9/2

  • Option 2)

    5/2

  • Option 3)

    7/2

  • Option 4)

    none

 

Answers (2)

best_answer

As we have learned

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

-

 

 

we have , On solving theequation 

9x^2+6bx = 16 \\9x^2+6bx-16 = 0

Also At (\alpha ,\beta ) [Point of intersection ]

2y \frac{dy}{dx}= 6 \Rightarrow \frac{dy}{dx}= \frac{3}{\beta }= m_1

and 18x + 2by\frac{dy}{dx }= 0 \Rightarrow \frac{dy}{dx }= \frac{-9x}{by}= \frac{-9\alpha }{b\beta }= m_2

So m_1 \times m_2 = -1

\Rightarrow \frac{3}{\beta }\times \frac{-9 \alpha }{b\beta } = -1 \\27 \alpha = b\beta ^2

Also 

\beta ^2 = 6 \alpha

so b = \frac{27 \alpha }{\beta ^2}= 27 /6 = 9/2

 

 


Option 1)

9/2

Option 2)

5/2

Option 3)

7/2

Option 4)

none

Posted by

Himanshu

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9/2

Posted by

Srivarshini pratha

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