Let \( y=y(x) \) be a function of \( x \) satisfying \( y \sqrt{1-x^{2}}=k -x \sqrt{1-y^{2}} \) where \( k \) is a const…

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

[JEE Main 2020, 7 Jan (Shift 2)]