The orthogonal trajectories of the curves `(x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1`, `lambda` being the parameter of the family is

Find the orthogonal trajectories of family of curves x^(2)+y^(2)=cx

Orthogonal trajectories of the family of curves x^2 + y^2 = c^2

Prove that the family of curves x^2/(a^2+lambda)+y^2/(b^2+lambda)=1 , where lambda is a parameter, is self orthogonal.

Prove that the tangents to family of hyperbola (x^(2))/(b^(2)+lambda)-(y^(2))/(b^(2))=1 (where lambda is a real parameter) at their point of intersection with x^(2)-y^(2)=2b^(2)+lambda^(2) are a pair of fixed lines. Find the equations of the lines.

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

Orthogonal trajectories of the family of curves x^(2)+y^(2)=a is an arbitrary constant is

Show that the curves (x^(2))/(a^(2)+lambda_(1))=1 and (x^(2))/(a^(2)+lambda_(2))+(y^(2))/(b^(2)+lambda_(2))=1 intersect at right angles.

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