Question

Find the differential equation for the family of curves
$x {}^{2} + y {}^{2} = a {}^{2}$
​

Answer 1

Answer:

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Step-by-step explanation:Given equation :

x  

2

=4b(y+b)

differentiate w.r.t x

2x=4b.  

dx

dy

​

 

x=2b  

dx

dy

​

 

b=  

2.  

dx

dy

​

 

x

​

 Put in given eq.

x  

2

=4.  

2  

dx

dy

​

 

x

​

.y+4  

⎝

⎜

⎜

⎛

​

 

2  

dx

dy

​

 

x

​

 

⎠

⎟

⎟

⎞

​

 

2

 

∴x(  

dx

dy

​

)  

2

=2y  

dx

dy

​

+x

∴x(y  

′

)  

2

=x+2yy  

Answer 2

Answer:

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