Let y=y(x) be a function of x satisfying y √(1-x^2)= k -x √(1-y^2) where k is a constant and y(1/2)=-1/4. Then (d y)/(d x) at x=1/2, is equal to:

Let $\displaystyle y=y(x)$ be a function of $\displaystyle x$ satisfying $\displaystyle y \sqrt{1-x^2}=\mathrm{k}-x \sqrt{1-y^2}$ where k is a constant and $\displaystyle y\left(\frac{1}{2}\right)=-\frac{1}{4}$. Then $\displaystyle \frac{\mathrm{d} y}{\mathrm{~d} x}$ at $\displaystyle x=\frac{1}{2}$, is equal to :