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

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

At the top of parabolic trajectory of projectile, the acceleration is

The equation of a circle C_1 is x^2+y^2= 4 . The locus of the intersection of orthogonal tangents to the circle is the curve C_2 and the locus of the intersection of perpendicular tangents to the curve C_2 is the curve C_3 , Then

Find the common factors of the given terms 2y,22xy.

Find the equation of the bisectors of the angle between the lines represented by 3x^2-5xy+4y^2=0

The unit vector which is orthogonal to the vector vec a = 3i+2j+6k and is coplanar with the vectors vec b = 2i+j+k and vec c = i-j+k is