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

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

Find the differential equation of the family of curves y=A e^(2x)+B e^(-2x) , where A and B are arbitrary constants.

Find the orthogonal trajectory of y^2=4a x (a being the parameter).

Find the differential equation of the family of curves represented by y^(2)-2ay+x^(2)=a^(2), where a is an arbitrary constant.

The differential equation for the family of curve x^2+y^2-2a y=0, where a is an arbitrary constant, is

The differential equation representing the family of curves y^2=2c(x+sqrt(c)), where c is a positive parameter, is of (A) order 1 (B) order 2 (C) degree 3 (D) degree 4

Find the angle of intersection of the curves x y=a^2a n dx^2+y^2=2a^2

If the differential equation representing the family of curves y=C_1 cos 2 x+C_2 cos ^2 x+C_3 sin ^2 x+C_4 is lambda y^(prime)=y^(prime prime) tan2 x , then lambda is

Find the ratio of the areas of two regions of the curve C_(1) -= 4x^(2) + pi^(2)y^(2) = 4pi^(2) divided by the curve C_(2) -= y = -(sgn(x - (pi)/(2)))cos x (where sgn (x) = signum (x)).

Which of the following is not the differential equation of family of curves whose tangent form an angle of pi/4 with the hyperbola xy= c^2 ? (a) dy/dx=(x-y)/(x+y) (b)dy/dx=(x)/(x-y) (c)dy/dx=(x+y)/(x-y) (d)N.O.T.