Question

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

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

Answer 1

The correct option is B

$yy\text{'}\text{'}+{(y\text{'})}^2+1=0$

Explanation for the correct option:

Differentiation of circle equation:

By differentiating $x^2+y^2=1$ w.r.t $x$, we get

$2x+2yy\text{'}=0$

Again differentiating it w.r.t $x$, we get

$\begin{array}{rcl}2+2\left(yy\text{'}\text{'}+y{\text{'}}^2\right)& =& 0\\ & \Rightarrow & 2\left(1+yy\text{'}\text{'}+y{\text{'}}^2\right)=0\\ \Rightarrow 1+yy\text{'}\text{'}+y{\text{'}}^2& =& 0\end{array}$

Hence, option B is correct.