If \( y \sqrt{1-x^{2}}=k-x \sqrt{1-y^{2}} \) and \( y\left(\frac{1}{2}\right)=-\frac{1}{4} \), t....

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If \( y \sqrt{1-x^{2}}=k-x \sqrt{1-y^{2}} \) and \( y\left(\frac{1}{2}\right)=-\frac{1}{4} \), then
\( \mathrm{P} \)
\( \frac{d y}{d x} \) at \( x=\frac{1}{2} \) is
(1) \( \frac{2}{\sqrt{5}} \)
(2) \( -\frac{\sqrt{5}}{4} \)
(3) \( -\frac{\sqrt{5}}{2} \)
(4) \( \frac{\sqrt{5}}{2} \)


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