For the curve $y=b{e}^{x/a}$

detailed solution

Correct option is C

The given curve is y = bex/a Let us consider a point (x1, y1) on the curve.Then,  y1=b ex1/a          …………….(1)Differentiating the curve  y=b ex/a  with respect to ‘x’ we get  dydx=b ex/a.1a ∴ (dydx)(x1,y1)=baex1/a Thus, the length of subtangent = |y1(dxdy)(x1,y1)| =|y1.abex1/a|=|bex1/a.abex1/a|= |a|   (constant)                                                                                         [ Using (i) and (ii) ]⇒  Subtangent is of constant length |a|Again, length of subnormal = |y1(dydx)(x1,y1)| = |b ex1/a.b ex1/aa| = 1|a|(b ex1/a)2=1|a|y2          ( using (i) )Therefore, subnormal varies as the square of ordinate.