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Differential Equations question

2019 · Shift 1 · Q23

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JEE Advanced
Mathematics
Differential Equations
2019 · Shift 1 · Q23

Differential Equations question

2019 · Shift 1 · Q23

JEE AdvancedMathematicsDifferential EquationsMultiple correct+4 / −1

Let

\Gamma

denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to I` at a point P intersect the y-axis at YP. If PYP has length 1 for each point P on I`, then which of the following options is/are correct?

A
$xy' + \sqrt {1 - {x^2}} = 0$
B
$xy' - \sqrt {1 - {x^2}} = 0$
C
$y = {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) - \sqrt {1 - {x^2}}$
D
$y = - {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) + \sqrt {1 - {x^2}}$

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