Math, asked by kmuthulakshmi473, 6 months ago

find the envelope of x^2/ a^2+ y^2/b^2=1 , where the parameter a are connected a^n+b^n=c^n, where c is a constant​

Answers

Answered by tejaswinimogal11
5

Answer:

Step-by-step explanation:

Let the equation of straight line be  

a

x

​  

+  

b

y

​  

=1    ....(1)

Given a+b=4    ....(2)

Differentiating eqn (1) w.r.t. a , we get

−  

a  

2

 

x

​  

−  

b  

2

 

y

​  

 

da

db

​  

=0      

⇒  

a  

2

 

x

​  

+  

b  

2

 

y

​  

 

da

db

​  

=0     ....(3)

Differentiating (2) w.r.. t a, we get

1+  

da

db

​  

=0

⇒  

da

db

​  

=−1      .....(4)

From (3) and (4), we get

a  

2

 

x

​  

=  

b  

2

 

y

​  

     ....(5)

⇒  

b

y

​  

 

a

x

​  

 

​  

=  

b

a

​  

 

Adding 1 to both sides, we get

⇒  

b

y

​  

 

1

​  

=  

b

4

​  

 

⇒b  

2

=4y

⇒b=2  

y

​  

 

Also, by eqn (5), we get

a=2  

x

​  

 

Now, using (2), the envelope is

x

​  

+  

y

​  

=2

Answered by tripathiakshita48
0

Answer:find the envelope of x^2/ a^2+ y^2/b^2=1 , where the parameter a are connected a^n+b^n=c^n, where c is a constant​ is x/a+y/b+z/c=1

Step-by-step explanation:

Let the equation of straight line be  

ax+ by=1    ....(1)

Given a+b=4    ....(2)

Differentiating eqn (1) w.r.t. a , we get

−  

a  2x−  b  2adb=0      

⇒  a2x+  b 2y

Now solving this differntial and getting the account is the same as solving:-

to get the final solutions and the envelope of x^2/ a^2+ y^2/b^2=1 at the given constraint of the ellipse that:-

So we know how to get the equation of the envelope that:-

3.1 Rolls Parallel to a Lateral Wall

In the direction of the pattern's wavevector, the envelope equation defines a well-posed second-order differential problem if we have one condition at each end of the interval corresponding to the width of the system. At lowest order we usually have

(11)

or, for a semi-infinite system,

Writing A(x) = |A(x)|exp(i ϕ(x)), we can get the steady solution explicitly; the equation for ϕ reads

which yields:-

So using this theoram we get the equation of the envelope as:-

Answer:-find the envelope of x^2/ a^2+ y^2/b^2=1 , where the parameter a are connected a^n+b^n=c^n, where c is a constant is x/a+y/b+z/c=1.

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