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if x^2+y^2=a^2then find the value of a Please answer as soon as possible.

if x^2+y^2=a^2then find the value of a
Please answer as soon as possible. 
 

Grade:11

1 Answers

Arun
25763 Points
one year ago

First find y'
y' = -x/y lets name it eq1
Then find y'' 
y'' = (-y + xy')/y^2
Substitute x in terms of y and y' from eq 1 we get
y'' = -(1 + y'^2)/y lets name it eq2
Substitute y' = -x/y
We get
y'' = -(x^2 + y^2)/y^3
Substitute x^2 + y^2 = a^2
y'' = -a^2/y^3
a^2 = -y^3 × y''
a = (-y^3 × y'')^(1/2)
a = |y| × (-yy'')^(1/2)
From eq 2 
1 + y'^2 = -yy''
and y = -(1 + y'^2)/y''
Therefore
a = |-(1 + y^2)/y''| (1 + y'^2)^(1/3)
We can write |-(1 + y^2)| = {(1 + y^3)^2}^(1/2)
Therefore 
a = {(1 + y'^2)^3}^(1/2)/|y''|

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