Math, asked by Jyothsna2130, 10 days ago

10. Problem: Form the differential equation corresponding to the family of circles passing
through the origin and having centres on Y-axis.​

Answers

Answered by Mashalbaigo
0

hii here is ur answer!!

ANSWER

It is given that, circles pass through origin and their centres lie on Y-axis.

Let (0,k) be the centre of the circle with k as its centre.

So, the equation of circle is

(x−0)  

2

+(y−k)  

2

=k  

2

 

x  

2

+(y−k)  

2

=k  

2

 

x  

2

+y  

2

−2ky=0

2y

x  

2

+y  

2

 

​  

=k      .....(1)

Differentiating equation 1 w.r.t. x, we get,

4y  

2

 

2y(2x+2y  

dx

y

​  

)−(x  

2

+y  

2

)  

dx

2dy

​  

 

​  

=0

4y(x+y  

dx

dy

​  

)−2(x  

2

+y  

2

)  

dx

dy

​  

=0

4xy=4y  

2

 

dx

dy

​  

−2(x  

2

+y  

2

)  

dx

dy

​  

=0

(4y  

2

−2x  

2

−2y  

2

)  

dx

dy

​  

+4xy=0

(2y  

2

−2x  

2

)  

dx

dy

​  

+4xy=0

(y  

2

−x  

2

)  

dx

dy

​  

+2xy=0

(x  

2

−y  

2

)  

dx

dy

​  

−2xy=0

hope helpful!!

:)

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