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A curve passes through origin. At any point P(x, y) lines are drawn parallel to co-ordinate axes. The area of the rectangle so formed is divided by the curve in the ratio 2 : 1 from left to right. Let C1, C2, ......... be such curves whose equations are y=f1(x),y=f2(x),..etc

 Questions Based on this write up

Q1: The family of the curves denoted by C1, C2, .............. are :
      (a) symmetric about x-axis             (b) symmetric about y-axis
      (c) symmetric about x = y              (d) nothing can be said in general.

Q2: If one such curve passes through (2, 1), the area bounded
       y = f (x), x-axis and x = 2 is :
       (a) 16/3                 (b) 2/3          
       (c) 1/3                   (d) None of these.

Q3: The curve has which of the following to be true ?
       (a) The tangent at any point is of constant length
       (b) The portion intercepted by normal is constant
       (c) Subnormal is constant
       (d) Subtangent is constant.

Q4: The curve is necessarily a :
       (a) logarithmic curve                               (b) ellipse
       (c) an exponential curve                          (d) None of these

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