Mathematics

Problem

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{dy}{dx}

x = \frac{1}{2}

is equal to: [JEE-MAIN ONLINE-2020] (1)

\frac{\sqrt{5}}{2}

(2)

-\frac{\sqrt{5}}{2}

(3)

\frac{2}{\sqrt{5}}

(4)

-\frac{\sqrt{5}}{4}