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Differentiation question

2020 · 7 Jan · Shift 2 · Q34

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PYQ Library
JEE Main
Mathematics
Differentiation
2020 · 7 Jan · Shift 2 · Q34

Differentiation question

2020 · 7 Jan · Shift 2 · Q34

JEE MainMathematicsDifferentiationMCQ+4 / −1

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( {{1 \over 2}} \right) = - {1 \over 4}

. Then

{{dy} \over {dx}}

at x =

{1 \over 2}

, is equal to :

A
${2 \over {\sqrt 5 }}$
B
$- {{\sqrt 5 } \over 2}$
C
${{\sqrt 5 } \over 2}$
D
$- {{\sqrt 5 } \over 4}$

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