If $x^2+y^2=1$, then:
Answer & explanation
Correct answer: option 2
$y^2=1-x^2 \Rightarrow 2 y y'=-2 x$
$\Rightarrow y y'=-x \Rightarrow y y''+y'+y'=-1$
$\Rightarrow y y''+\left(y'\right)^2+1=0$
Hence (2) is correct answer.
If $x^2+y^2=1$, then:
Correct answer: option 2
$y^2=1-x^2 \Rightarrow 2 y y'=-2 x$
$\Rightarrow y y'=-x \Rightarrow y y''+y'+y'=-1$
$\Rightarrow y y''+\left(y'\right)^2+1=0$
Hence (2) is correct answer.