Find the orthogonal trajectories of `xy = c`

The equation to the orthogonal trajectories of the system of parabolas y=ax^2 is

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

The orthogonal trajectories of the circle x^(2)+y^(2)-ay=0 , (where a is a parameter), 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

If M and N are orthogonal matrices of order 3, then which of the following is (are) orthogonal matrix?

A person can not see object in two orthogonal direction clearly. It can be removed by using cylindrical lens in particular direction.

Find the differential equation of xy = ae^x + be^(-x) .

The orthogonal projection A' of the point A with position vector (1, 2, 3) on the plane 3x-y+4z=0 is

If A is a orthogonal matrix, then