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).