Find the orthogonal trajectories of family of curves `x^2+y^2=c x`

Find the orthogonal trajectories of xy=c .

The orthogonal trajectories of the family of curves y=Cx^(2) , (C is an arbitrary constant), is

The orthogonal trajectories of the family of curves a^(n-1)y = x^n are given by

STATEMENT-1 : The orthogonal trajectory of a family of circles touching x-axis at origin and whose centre the on y-axis is self orthogonal. and STATEMENT-2 : In order to find the orthogonal trajectory of a family of curves we put -(dx)/(dy) in place of (dy)/(dx) in the differential equation of the given family of curves.

The orthogonal trajectories of the family of curves an a^(n-1)y = x^n are given by (A) x^n+n^2y=constant (B) ny^2+x^2=constant (C) n^2x+y^n=constant (D) y=x

The orthogonal trajectories of the family of curves y=a^nx^n are given by (A) n^2x^2+y^2 = constant (B) n^2y^2+x^2 = constant (C) a^nx^2+n^2y^2 = constant (D) none of these

The orthogonal trajectories of the family of circles given by x^2 + y^2 - 2ay = 0 , is

Orthogonal trajectories of family of the curve x^(2/3)+y^(2/3)=a^((2/3)) , where a is any arbitrary constant, is

The value of k such that the family of parabolas y=cx^(2)+k is the orthogonal trajectory of the family of ellipse x^(2)+2y^(2)-y=c, is

The orthogonal trajectories to the family of curve y= cx^(K) are given by :