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Segment of the tangent to the curve $x y = c^{2}$ at the points $(x', y')$ which is contained between the co-ordinate axes, is bisected at the point:

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(−x',−y')

(y',x')

(x'/2,y'/2)

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Correct option is D

[dydx](x',y')=−c2x'2=−y'x' ∴ Equation of tangent at (x',y') isy−y'=(−y'/x')(x−x')Which meets the co-ordinates axes at Aand B(say).Then A=(2x',0),B=(0,2y').Mid-point of AB=(x',y').

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Segment of the tangent to the curve xy=c2 at the points (x',y')which is contained between the co-ordinate axes, is bisected at the point:

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Segment of the tangent to the curve $x y = c^{2}$ at the points $(x', y')$ which is contained between the co-ordinate axes, is bisected at the point: