Area Bounded by

Tangent to xy=c2 & x-y Axis

The area of triangle OAB bounded by the tangent to xy=c2 in the 1st quadrant, x-axis & y-axis is (refer figure):

(1) Maximum if P is the midpoint of AB
(2) Increases as P moves downwards or upwards
(3) Constant
(4) Independent of c

Solution

xy=c2 is rectangular hyperbola. The equation of tangent in parametric form at some point P (ct,ct) is given by,

xt+yt=2c

At point A, x=2ct=OA

At point B, y=2ct=OB

Area of ΔOAB = 12.OA.OB = 12.2ct.2ct = 2c2

Hence, Option (3).

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