Question

If the curve yo = 6X, 9X2 + by? - 16 intersect each other at right angles, then the value of b
is:
....​

Answer 1

Step-by-step explanation:

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Answer 2

It is given that the curves y  

2

=6x and 9x  

2

+by  

2

=16 intersect at right angles.

Let the slope of y  

2

=6x be m  

1

​  

 

Also, let the slope of 9x  

2

+by  

2

=16 be m  

2

​  

 

Thus, we have m  

1

​  

m  

2

​  

=−1

Differentiating both the equations wrt x we get

2y  

dx

dy

​  

=6

Or, ym  

1

​  

=3........(1)

Also, 18x+2by  

dx

dy

​  

=0

Or, m  

2

​  

=  

by

−9x

​  

 

We know that m  

1

​  

m  

2

​  

=−1

Thus,  

y

3

​  

×  

by

−9x

​  

=1

→b=  

y  

2

 

27x

​  

 

Putting y  

2

=6x in the above equation we get

b=  

6x

27x

​  

=  

2

9

​