Question

If $ x^2 + y^2 = 1$, then

• A. $ yy'' - 2 (y' )^2 + 1 = 0 $
• B. $ yy'' + (y' )^2 + 1 = 0 $
• C. $ yy'' + (y' )^2 - 1 = 0 $
• D. $ yy'' + 2 (y' )^2 + 1 = 0 $

Answer 1

Answer: (B)

Given, $ x^2 + y^2 = 1$
On differentiating w.r.t. $x$, we get
$2 x + 2 yy ' = 0$
$\Rightarrow x + yy' = 0 $
Again, differentiating w.r.t. $x$, we get
$1 + y ' y' + yy" = 0$
$\Rightarrow 1 + (y')^2 + yy" = 0 $