Which of the following does not represent the orthogonal trajectory of the system of curves (dydx)2=ax

[d] The family of curves which are orthogonal (i.e. intersect at right angles) to a given system of curves is obtained by substitute −dxdy for dydx in the differential equation of the given system, The given differential equation is (dydx)2=ax Replacing dydxby −dxdy, we get (dxdy)2=ax⇒(dydx)2=xa⇒dydx=±xa.−−−√ Integrating we get, y+c=±23a√x3/2   ? (i) ⇒(y+c)2=49ax3⇒9a(y+c)2=4x3        .. (ii) From (i) and (ii) all of the first three given option represent required equations.